Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
7101	Solve by Substitution	x+3y=1 , -3x-5y=-2	$x + 3 y = 1$ , $- 3 x - 5 y = - 2$
7102	Solve Using an Augmented Matrix	x+2y-z=4 , 2x+y+z=-2 , x+2y+z=2	$x + 2 y - z = 4$ , $2 x + y + z = - 2$ , $x + 2 y + z = 2$
7103	Solve Using an Augmented Matrix	x+3y-z=4 , 3y-z=0 , x-y+5z=0	$x + 3 y - z = 4$ , $3 y - z = 0$ , $x - y + 5 z = 0$
7104	Simplify the Matrix	[[1,2,3],[4,5,6]]*[[-1,2],[2,3],[1,0]]-[[7,6],[8,5]]	$[\begin{array}{c} 1 & 2 & 3 \\ 4 & 5 & 6 \end{array}] \cdot [\begin{array}{c} - 1 & 2 \\ 2 & 3 \\ 1 & 0 \end{array}] - [\begin{array}{c} 7 & 6 \\ 8 & 5 \end{array}]$
7105	Simplify the Matrix	fourth root of 100m^12n^4 , m>=0 , n>=0	$\sqrt[4]{100 m^{12} n^{4}}$ , $m \geq 0$ , $n \geq 0$
7106	Find Reduced Row Echelon Form	[[2,3,3,-1,-4,2,5,0,1,4],[1,5,2,0,0,0,1,-2,-3,-4]]	$[\begin{array}{c} 2 & 3 & 3 & - 1 & - 4 & 2 & 5 & 0 & 1 & 4 \\ 1 & 5 & 2 & 0 & 0 & 0 & 1 & - 2 & - 3 & - 4 \end{array}]$
7107	Solve using Gaussian Elimination	x_1-2x_2+3x_3=11 4x_1+x_2-x_3=4 2x_1-x_2+3x_3=10	$x_{1} - 2 x_{2} + 3 x_{3} = 11$ $4 x_{1} + x_{2} - x_{3} = 4$ $2 x_{1} - x_{2} + 3 x_{3} = 10$
7108	Find the Cube Roots of a Complex Number	-8i	$- 8 i$
7109	Solve using Gaussian Elimination	3x+2y+z=1 5x+3y+4z=2 x+y-z=1	$3 x + 2 y + z = 1$ $5 x + 3 y + 4 z = 2$ $x + y - z = 1$
7110	Solve Using a Matrix by Elimination	-3x+y-z=-2 , -3x+z=4 , y-5z=0	$- 3 x + y - z = - 2$ , $- 3 x + z = 4$ , $y - 5 z = 0$
7111	Simplify the Matrix	R=[[3,2],[-1,0]] , S=[[-2,1],[1,-1]]	$R = [\begin{array}{c} 3 & 2 \\ - 1 & 0 \end{array}]$ , $S = [\begin{array}{c} - 2 & 1 \\ 1 & - 1 \end{array}]$
7112	Solve Using a Matrix by Row Operations	x+2y-z=4 , 2x+y+z=-2 , x+2y+z=2	$x + 2 y - z = 4$ , $2 x + y + z = - 2$ , $x + 2 y + z = 2$
7113	Solve Using a Matrix by Row Operations	1/2x-y=-3 , 9x-y=1	$\frac{1}{2} x - y = - 3$ , $9 x - y = 1$
7114	Solve using Gaussian Elimination	3x_1+6x_2-6x_3=9 2x_1-5x_2+4x_3=6 -x_1+16x_2-14x_3=-3	$3 x_{1} + 6 x_{2} - 6 x_{3} = 9$ $2 x_{1} - 5 x_{2} + 4 x_{3} = 6$ $- x_{1} + 16 x_{2} - 14 x_{3} = - 3$
7115	Simplify the Matrix	square root of 50x^2 = square root of 252x^2=5x square root of b	$\sqrt{50 x^{2}} = \sqrt{25 \cdot 2 \cdot x^{2}} = 5 x \sqrt{b}$
7116	Solve Using a Matrix by Row Operations	x+3y-z=4 , 3y-z=0 , x-y+5z=0	$x + 3 y - z = 4$ , $3 y - z = 0$ , $x - y + 5 z = 0$
7117	Simplify the Matrix	(1,0m^3n^12)	$(1, 0 m^{3} n^{12})$
7118	Solve using Gaussian Elimination	2x_1+4x_2+6x_3=18 4x_1+5x_2-6x_3=24 2x_1+x_2-12x_3=6	$2 x_{1} + 4 x_{2} + 6 x_{3} = 18$ $4 x_{1} + 5 x_{2} - 6 x_{3} = 24$ $2 x_{1} + x_{2} - 12 x_{3} = 6$
7119	Find the Cube Roots of a Complex Number	1+i	$1 + i$
7120	Simplify the Matrix	Find RS if R=[[3,2],[-1,0]] , S=[[-2,1],[1,-1]]	Find $R S$ if $R = [\begin{array}{c} 3 & 2 \\ - 1 & 0 \end{array}]$ , $S = [\begin{array}{c} - 2 & 1 \\ 1 & - 1 \end{array}]$
7121	Solve Using a Matrix with Cramer's Rule	3z+3x+3y=19 , x+3=y , z=y-4x+1	$3 z + 3 x + 3 y = 19$ , $x + 3 = y$ , $z = y - 4 x + 1$
7122	Solve Using a Matrix by Row Operations	x-y=9 , x+y=6	$x - y = 9$ , $x + y = 6$
7123	Find the Inverse	[[0,-1,4],[6,0,-2],[1,0,0]]	$[\begin{array}{c} 0 & - 1 & 4 \\ 6 & 0 & - 2 \\ 1 & 0 & 0 \end{array}]$
7124	Solve using Gaussian Elimination	x_1+x_2-x_3=7 4x_1-x_2+5x_3=4 2x_1+2x_2-3x_3=0	$x_{1} + x_{2} - x_{3} = 7$ $4 x_{1} - x_{2} + 5 x_{3} = 4$ $2 x_{1} + 2 x_{2} - 3 x_{3} = 0$
7125	Find the Cube Roots of a Complex Number	8i	$8 i$
7126	Find the Null Space	S={[[2],[-1],[3],[1],[2]],[[1],[2],[-1],[5],[2]],[[2],[1],[-3],[6],[1]]}	$S = {[\begin{array}{c} 2 \\ - 1 \\ 3 \\ 1 \\ 2 \end{array}], [\begin{array}{c} 1 \\ 2 \\ - 1 \\ 5 \\ 2 \end{array}], [\begin{array}{c} 2 \\ 1 \\ - 3 \\ 6 \\ 1 \end{array}]}$
7127	Solve Using a Matrix with Cramer's Rule	y=3x+z-2 , z=3x+4 , y=5z	$y = 3 x + z - 2$ , $z = 3 x + 4$ , $y = 5 z$
7128	Solve Using a Matrix with Cramer's Rule	5x+3=4y , y=8x-2	$5 x + 3 = 4 y$ , $y = 8 x - 2$
7129	Solve using Gaussian Elimination	9x_1+9x_2-7x_3=6 -7x_1-x_3=-10 9x_1+6x_2+8x_3=45	$9 x_{1} + 9 x_{2} - 7 x_{3} = 6$ $- 7 x_{1} - x_{3} = - 10$ $9 x_{1} + 6 x_{2} + 8 x_{3} = 45$
7130	Find the Null Space	S={[[2],[-1],[3],[1],[0],[3]],[[9],[-6],[-2],[3],[2],[1]],[[1],[1],[1],[0],[0],[1]],[[-3],[1],[4],[2],[1],[2]]}	$S = {[\begin{array}{c} 2 \\ - 1 \\ 3 \\ 1 \\ 0 \\ 3 \end{array}], [\begin{array}{c} 9 \\ - 6 \\ - 2 \\ 3 \\ 2 \\ 1 \end{array}], [\begin{array}{c} 1 \\ 1 \\ 1 \\ 0 \\ 0 \\ 1 \end{array}], [\begin{array}{c} - 3 \\ 1 \\ 4 \\ 2 \\ 1 \\ 2 \end{array}]}$
7131	Solve using Gaussian Elimination	-2x_1-6x_2-3x_3=9 -x_1+x_2-x_3=1 x_1-x_2+2x_3=2	$- 2 x_{1} - 6 x_{2} - 3 x_{3} = 9$ $- x_{1} + x_{2} - x_{3} = 1$ $x_{1} - x_{2} + 2 x_{3} = 2$
7132	Solve using Gaussian Elimination	x+3y-4z=2 3x+10y-12z=8 9x+28y-36z=20	$x + 3 y - 4 z = 2$ $3 x + 10 y - 12 z = 8$ $9 x + 28 y - 36 z = 20$
7133	Solve using Gaussian Elimination	x+y+z=6 2x-y-z=3 x+2y+2z=0	$x + y + z = 6$ $2 x - y - z = 3$ $x + 2 y + 2 z = 0$
7134	Solve using Gaussian Elimination	x+y+z=-6 2x+y-z=-1 x-2y+3z=-6	$x + y + z = - 6$ $2 x + y - z = - 1$ $x - 2 y + 3 z = - 6$
7135	Solve using Gaussian Elimination	3x_1+6x_2-6x_3=9 2x_1-5x_2+4x_3=6 5x_1+28x_2-26x_3=-8	$3 x_{1} + 6 x_{2} - 6 x_{3} = 9$ $2 x_{1} - 5 x_{2} + 4 x_{3} = 6$ $5 x_{1} + 28 x_{2} - 26 x_{3} = - 8$
7136	Solve using Gaussian Elimination	-2x_1+x_2+6x_3=18 5x_1+8x_3=-16 3x_1+2x_2-10x_3=-3	$- 2 x_{1} + x_{2} + 6 x_{3} = 18$ $5 x_{1} + 8 x_{3} = - 16$ $3 x_{1} + 2 x_{2} - 10 x_{3} = - 3$
7137	Simplify the Matrix	5 cube root of 1,250+7 cube root of 270	$5 \sqrt[3]{1, 250} + 7 \sqrt[3]{270}$
7138	Solve the Matrix Equation	[[32,10],[3/5,1/8]]*F=[[-80,80],[1,2]]	$[\begin{array}{c} 32 & 10 \\ \frac{3}{5} & \frac{1}{8} \end{array}] \cdot F = [\begin{array}{c} - 80 & 80 \\ 1 & 2 \end{array}]$
7139	Simplify the Matrix	square root of x^12y^9z^5 = square root of x^12y^8yz^4z=x^ay^bz^c square root of yz	$\sqrt{x^{12} y^{9} z^{5}} = \sqrt{x^{12} \cdot y^{8} \cdot y \cdot z^{4} \cdot z} = x^{a} y^{b} z^{c} \sqrt{y z}$
7140	Solve the Matrix Equation	[[1/9,6],[1/3,27]]*B=[[-10,7],[-48,30]]	$[\begin{array}{c} \frac{1}{9} & 6 \\ \frac{1}{3} & 27 \end{array}] \cdot B = [\begin{array}{c} - 10 & 7 \\ - 48 & 30 \end{array}]$
7141	Simplify the Matrix	(f(x+h)-f(x))/h , h!=0	$\frac{f (x + h) - f (x)}{h}$ , $h \neq 0$
7142	Find Reduced Row Echelon Form	[[-1,0,-2,x_1],[2,3,-1,x_2],[0,-1,-3,x_3]]	$[\begin{array}{c} - 1 & 0 & - 2 & x_{1} \\ 2 & 3 & - 1 & x_{2} \\ 0 & - 1 & - 3 & x_{3} \end{array}]$
7143	Solve using Gaussian Elimination	2x+6y+z=7 x+2y-z=-1 5x+7y-4z=9	$2 x + 6 y + z = 7$ $x + 2 y - z = - 1$ $5 x + 7 y - 4 z = 9$
7144	Solve using Gaussian Elimination	3x-12y+15z=10 -4x+16y-20z=-12	$3 x - 12 y + 15 z = 10$ $- 4 x + 16 y - 20 z = - 12$
7145	Simplify the Matrix	(7^2*7^8)/(7^4)=(7^a)/(7^4)=7^b	$\frac{7^{2} \cdot 7^{8}}{7^{4}} = \frac{7^{a}}{7^{4}} = 7^{b}$
7146	Solve using Gaussian Elimination	5x+2y+z=-11 2x-3y-z=17 7x-y=12	$5 x + 2 y + z = - 11$ $2 x - 3 y - z = 17$ $7 x - y = 12$
7147	Solve using Gaussian Elimination	2x_1+4x_2+6x_3=18 4x_1+5x_2-6x_3=24 2x_1+x_2-12x_3=2	$2 x_{1} + 4 x_{2} + 6 x_{3} = 18$ $4 x_{1} + 5 x_{2} - 6 x_{3} = 24$ $2 x_{1} + x_{2} - 12 x_{3} = 2$
7148	Find the Cube Roots of a Complex Number	27i	$27 i$
7149	Solve using Gaussian Elimination	x_1+2x_2-4x_3=4 -2x_1-4x_2+8x_3=-8	$x_{1} + 2 x_{2} - 4 x_{3} = 4$ $- 2 x_{1} - 4 x_{2} + 8 x_{3} = - 8$
7150	Simplify the Matrix	[[2],[-6]]-[[-3],[2]]+[[6],[0]]	$[\begin{array}{c} 2 \\ - 6 \end{array}] - [\begin{array}{c} - 3 \\ 2 \end{array}] + [\begin{array}{c} 6 \\ 0 \end{array}]$
7151	Solve using Gaussian Elimination	x+4y=4 2x+9y=11 5x+24y=32	$x + 4 y = 4$ $2 x + 9 y = 11$ $5 x + 24 y = 32$
7152	Solve using Gaussian Elimination	3x+y-z=5 x+2y=8 y-2z=-5	$3 x + y - z = 5$ $x + 2 y = 8$ $y - 2 z = - 5$
7153	Find the Square Roots of a Complex Number	4i	$4 i$
7154	Solve using Gaussian Elimination	4x-3y+z=-8 -2x+y-3z=-4 x-y+2z=3	$4 x - 3 y + z = - 8$ $- 2 x + y - 3 z = - 4$ $x - y + 2 z = 3$
7155	Find the Cube Roots of a Complex Number	125i	$125 i$
7156	Solve Using an Augmented Matrix	2x-3y+z=4 y-2z+x-5=0 3-2x=4y-z	$2 x - 3 y + z = 4$ $y - 2 z + x - 5 = 0$ $3 - 2 x = 4 y - z$
7157	Solve Using an Augmented Matrix	-2x_1-6x_2-3x_3=9 -x_1+x_2-x_3=1 x_1-x_2+2x_3=2	$- 2 x_{1} - 6 x_{2} - 3 x_{3} = 9$ $- x_{1} + x_{2} - x_{3} = 1$ $x_{1} - x_{2} + 2 x_{3} = 2$
7158	Find Reduced Row Echelon Form	[[0,1,-2,1,1,5],[-2,3,-6,0,6,9],[1,1,-2,0,2,3]]	$[\begin{array}{c} 0 & 1 & - 2 & 1 & 1 & 5 \\ - 2 & 3 & - 6 & 0 & 6 & 9 \\ 1 & 1 & - 2 & 0 & 2 & 3 \end{array}]$
7159	Find the Square Roots of a Complex Number	3(cos(pi)+isin(pi))	$3 (\cos (π) + i \sin (π))$
7160	Find the Fourth Roots of a Complex Number	-4-4i	$- 4 - 4 i$
7161	Solve the Matrix Equation	x=[[0,2,4,6],[0,3,6,9],[0,4,8,12]]	$x = [\begin{array}{c} 0 & 2 & 4 & 6 \\ 0 & 3 & 6 & 9 \\ 0 & 4 & 8 & 12 \end{array}]$
7162	Find the Square Roots of a Complex Number	-3+4i	$- 3 + 4 i$
7163	Find the Fourth Roots of a Complex Number	3(cos(pi)+isin(pi))	$3 (\cos (π) + i \sin (π))$
7164	Simplify the Matrix	([(1,4-0,2)*3,2])÷1 , 5	$[(1, 4 - 0, 2) \times 3, 2] \div 1$ , $5$
7165	Find the Cube Roots of a Complex Number	3(cos(pi)+isin(pi))	$3 (\cos (π) + i \sin (π))$
7166	Determine if Linearly Dependent	B={[[-1],[4],[7]],[[6],[-5],[8]],[[1],[5],[9]]}	$B = {[\begin{array}{c} - 1 \\ 4 \\ 7 \end{array}], [\begin{array}{c} 6 \\ - 5 \\ 8 \end{array}], [\begin{array}{c} 1 \\ 5 \\ 9 \end{array}]}$
7167	Determine if Linearly Dependent	[[2],[-1],[4],[1],[2]] , [[1],[2],[-1],[5],[2]] , [[2],[1],[-3],[6],[1]]	$[\begin{array}{c} 2 \\ - 1 \\ 4 \\ 1 \\ 2 \end{array}]$ , $[\begin{array}{c} 1 \\ 2 \\ - 1 \\ 5 \\ 2 \end{array}]$ , $[\begin{array}{c} 2 \\ 1 \\ - 3 \\ 6 \\ 1 \end{array}]$
7168	Simplify the Matrix	x/a+x/b=c , a!=0 , b!=0 , a!=-b	$\frac{x}{a} + \frac{x}{b} = c$ , $a \neq 0$ , $b \neq 0$ , $a \neq - b$
7169	Simplify the Matrix	square root of 2 , square root of 8	$\sqrt{2}$ , $\sqrt{8}$
7170	Determine if Linearly Dependent	[[1,2,1],[3,-1,0],[6,-2,0]]	$[\begin{array}{c} 1 & 2 & 1 \\ 3 & - 1 & 0 \\ 6 & - 2 & 0 \end{array}]$
7171	Determine if Linearly Dependent	[[-1,6,1],[4,-5,5],[7,8,9]]	$[\begin{array}{c} - 1 & 6 & 1 \\ 4 & - 5 & 5 \\ 7 & 8 & 9 \end{array}]$
7172	Find the Norm	[[4],[0],[4],[5],[6],[7],[8]]	$[\begin{array}{c} 4 \\ 0 \\ 4 \\ 5 \\ 6 \\ 7 \\ 8 \end{array}]$
7173	Determine if Linearly Dependent	[[-1],[4],[7]] , [[6],[-5],[8]] , [[1],[5],[9]]	$[\begin{array}{c} - 1 \\ 4 \\ 7 \end{array}]$ , $[\begin{array}{c} 6 \\ - 5 \\ 8 \end{array}]$ , $[\begin{array}{c} 1 \\ 5 \\ 9 \end{array}]$
7174	Solve using Gaussian Elimination	2x-3y+z=4 y-2z+x-5=0 3-2x=4y-z	$2 x - 3 y + z = 4$ $y - 2 z + x - 5 = 0$ $3 - 2 x = 4 y - z$
7175	Determine if Linearly Dependent	[[1,2,1],[8,1,10],[6,2,5]]	$[\begin{array}{c} 1 & 2 & 1 \\ 8 & 1 & 10 \\ 6 & 2 & 5 \end{array}]$
7176	Solve Using an Augmented Matrix	3x-5y+z=14 2x+3y-4z=20 5x-y+2z=7	$3 x - 5 y + z = 14$ $2 x + 3 y - 4 z = 20$ $5 x - y + 2 z = 7$
7177	Find the Square Roots of a Complex Number	4+4i	$4 + 4 i$
7178	Find the Square Roots of a Complex Number	8(cos(pi/2)+isin(pi/2))	$8 (\cos (\frac{π}{2}) + i \sin (\frac{π}{2}))$
7179	Solve Using a Matrix with Cramer's Rule	2x-3y+z=4 y-2z+x-5=0 3-2x=4y-z	$2 x - 3 y + z = 4$ $y - 2 z + x - 5 = 0$ $3 - 2 x = 4 y - z$
7180	Find the Square Roots of a Complex Number	-4-4i	$- 4 - 4 i$
7181	Simplify the Matrix	((10x^3y^2)/(5x^-3y^4))^-3 , x!=0 , y!=0	${(\frac{10 x^{3} y^{2}}{5 x^{- 3} y^{4}})}^{- 3}$ , $x \neq 0$ , $y \neq 0$
7182	Find the Norm	[[4],[0],[4],[5],[6]]	$[\begin{array}{c} 4 \\ 0 \\ 4 \\ 5 \\ 6 \end{array}]$
7183	Find the Cube Roots of a Complex Number	8(cos(pi/2)+isin(pi/2))	$8 (\cos (\frac{π}{2}) + i \sin (\frac{π}{2}))$
7184	Simplify the Matrix	M=((x^5)^0x^8(x^2)^3)/((x*x)^5) , x!=0	$M = \frac{{(x^{5})}^{0} x^{8} {(x^{2})}^{3}}{{(x \cdot x)}^{5}}$ , $x \neq 0$
7185	Simplify the Matrix	cube root of 3 , cube root of 24	$\sqrt[3]{3}$ , $\sqrt[3]{24}$
7186	Simplify the Matrix	((a^2b^-3)/(a^-2b^2))^2 , a!=0 , b!=0	${(\frac{a^{2} b^{- 3}}{a^{- 2} b^{2}})}^{2}$ , $a \neq 0$ , $b \neq 0$
7187	Simplify the Matrix	p(x):\|5x+1\|=-6 q(x):\|x-1/2\|=2	$p (x) : \| 5 x + 1 \| = - 6$ $q (x) : \| x - \frac{1}{2} \| = 2$
7188	Solve using Gaussian Elimination	9x_2-7x_3=2 -x_3=-2 -3x_1+6x_2+8x_3=1	$9 x_{2} - 7 x_{3} = 2$ $- x_{3} = - 2$ $- 3 x_{1} + 6 x_{2} + 8 x_{3} = 1$
7189	Find the Fourth Roots of a Complex Number	8(cos(pi/2)+isin(pi/2))	$8 (\cos (\frac{π}{2}) + i \sin (\frac{π}{2}))$
7190	Simplify the Matrix	(2x+10)/(x^2+x-2)+2/(x+2)+x/(x-1) , x!=-2 , 1	$\frac{2 x + 10}{x^{2} + x - 2} + \frac{2}{x + 2} + \frac{x}{x - 1}$ , $x \neq - 2$ , $1$
7191	Solve Using an Inverse Matrix	x+y+z+t=4 , 2x-y-z-t=-1 , x+y-2z=0 , 3x+3t=6	$x + y + z + t = 4$ , $2 x - y - z - t = - 1$ , $x + y - 2 z = 0$ , $3 x + 3 t = 6$
7192	Find the Cube Roots of a Complex Number	-3+4i	$- 3 + 4 i$
7193	Simplify the Matrix	[[0,0],[0,0]]-[[x,y],[z,w]]	$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] - [\begin{array}{c} x & y \\ z & w \end{array}]$
7194	Find the Square Roots of a Complex Number	-3+3 square root of 3i	$- 3 + 3 \sqrt{3} i$
7195	Solve using Gaussian Elimination	x_1-3x_2+5x_3=18 2x_1+3x_2-4x_3=-5 x_1-x_2+2x_3=9	$x_{1} - 3 x_{2} + 5 x_{3} = 18$ $2 x_{1} + 3 x_{2} - 4 x_{3} = - 5$ $x_{1} - x_{2} + 2 x_{3} = 9$
7196	Simplify the Matrix	Given (x+5)/(x-1) if x<=-3 4x+9 if x>-3 ; what is 2(g(3))+g(-4) ?	Given $\frac{x + 5}{x - 1}$ if $x \leq - 3$ $4 x + 9$ if $x > - 3$ ; what is $2 (g (3)) + g (- 4)$ ?
7197	Simplify the Matrix	x>=0 : square root of 5x( square root of 8x^2-2 square root of x)	$x \geq 0$ : $\sqrt{5 x} (\sqrt{8 x^{2}} - 2 \sqrt{x})$
7198	Simplify the Matrix	p(x):\|1+2x\|=7 q(x):\|x-3\|=1-x	$p (x) : \| 1 + 2 x \| = 7$ $q (x) : \| x - 3 \| = 1 - x$
7199	Find the Square Roots of a Complex Number	5+2i	$5 + 2 i$
7200	Simplify the Matrix	(a^3b^-2)/(ab^-4) , a!=0 , b!=0	$\frac{a^{3} b^{- 2}}{a b^{- 4}}$ , $a \neq 0$ , $b \neq 0$