Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
101	Solve Using an Inverse Matrix	x+3y=-6 , 3x+2y=3	$x + 3 y = - 6$ $x + 3 y = - 6$ , $3 x + 2 y = 3$ $3 x + 2 y = 3$
102	Solve Using an Inverse Matrix	x+2y=1 , 5y=15	$x + 2 y = 1$ $x + 2 y = 1$ , $5 y = 15$ $5 y = 15$
103	Solve Using an Inverse Matrix	2x-6y=7 , 5x+2y=10	$2 x - 6 y = 7$ $2 x - 6 y = 7$ , $5 x + 2 y = 10$ $5 x + 2 y = 10$
104	Find the Result of 2 Times the 2x2 Identity Matrix	2	$2$ $2$
105	Find the Result of 3 Times the 3x3 Identity Matrix	3	$3$ $3$
106	Find the 7x7 Identity Matrix	7	$7$ $7$
107	Find the 9x9 Identity Matrix	9	$9$ $9$
108	Find the Result of 5 Times the 5x5 Identity Matrix	5	$5$ $5$
109	Solve Using an Inverse Matrix	x-z+3y=4 , z=3y , y-x=5z	$x - z + 3 y = 4$ $x - z + 3 y = 4$ , $z = 3 y$ $z = 3 y$ , $y - x = 5 z$ $y - x = 5 z$
110	Solve Using an Inverse Matrix	x-y=3 , 4x+y=17	$x - y = 3$ $x - y = 3$ , $4 x + y = 17$ $4 x + y = 17$
111	Solve Using an Inverse Matrix	x-y=7 , x-y=5	$x - y = 7$ $x - y = 7$ , $x - y = 5$ $x - y = 5$
112	Solve Using an Inverse Matrix	x-2y=3 , -2x+4y=6	$x - 2 y = 3$ $x - 2 y = 3$ , $- 2 x + 4 y = 6$ $- 2 x + 4 y = 6$
113	Solve Using an Inverse Matrix	x+y=48 , x=8y	$x + y = 48$ $x + y = 48$ , $x = 8 y$ $x = 8 y$
114	Solve Using an Inverse Matrix	x+y=6 , 2x-3y=2	$x + y = 6$ $x + y = 6$ , $2 x - 3 y = 2$ $2 x - 3 y = 2$
115	Solve Using an Inverse Matrix	x-3y=-6 , 5x+3y=42	$x - 3 y = - 6$ $x - 3 y = - 6$ , $5 x + 3 y = 42$ $5 x + 3 y = 42$
116	Solve Using an Inverse Matrix	x-y=-2 , 7x+3y=-66	$x - y = - 2$ $x - y = - 2$ , $7 x + 3 y = - 66$ $7 x + 3 y = - 66$
117	Solve Using an Inverse Matrix	y=3x+1 , 3y-4x=13	$y = 3 x + 1$ $y = 3 x + 1$ , $3 y - 4 x = 13$ $3 y - 4 x = 13$
118	Solve Using an Inverse Matrix	x+y=6 , x-y=2	$x + y = 6$ $x + y = 6$ , $x - y = 2$ $x - y = 2$
119	Solve Using an Inverse Matrix	x+y=19 , x-4y=-1	$x + y = 19$ $x + y = 19$ , $x - 4 y = - 1$ $x - 4 y = - 1$
120	Solve Using an Inverse Matrix	x+y+z=8 , 2x-y-z=10 , x-2y-3z=22	$x + y + z = 8$ $x + y + z = 8$ , $2 x - y - z = 10$ $2 x - y - z = 10$ , $x - 2 y - 3 z = 22$ $x - 2 y - 3 z = 22$
121	Solve Using an Inverse Matrix	x-3z=-2 , 2x+2y+z=4 , 3x+y-2z=5	$x - 3 z = - 2$ $x - 3 z = - 2$ , $2 x + 2 y + z = 4$ $2 x + 2 y + z = 4$ , $3 x + y - 2 z = 5$ $3 x + y - 2 z = 5$
122	Find the Dimensions	[[0,1,0],[0,0,1],[125x^3,-75x^2,15x]]	$⎡ ⎢ ⎣ \begin{matrix} 0 & 1 & 0 0 & 0 & 1 125 x^{3} & - 75 x^{2} & 15 x \end{matrix} ⎤ ⎥ ⎦$ $[\begin{array}{c} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 125 x^{3} & - 75 x^{2} & 15 x \end{array}]$
123	Solve Using an Inverse Matrix	y=3.2+x , 7.1-x=7.2y	$y = 3.2 + x$ $y = 3.2 + x$ , $7.1 - x = 7.2 y$ $7.1 - x = 7.2 y$
124	Find the 2x2 Identity Matrix	2	$2$ $2$
125	Solve the Matrix Equation	-3x+[[7,0,-1],[2,-3,4]]=[[10,0,8],[-19,-18,10]]	$- 3 x + [\begin{matrix} 7 & 0 & - 1 2 & - 3 & 4 \end{matrix}] = [\begin{matrix} 10 & 0 & 8 - 19 & - 18 & 10 \end{matrix}]$ $- 3 x + [\begin{array}{c} 7 & 0 & - 1 \\ 2 & - 3 & 4 \end{array}] = [\begin{array}{c} 10 & 0 & 8 \\ - 19 & - 18 & 10 \end{array}]$
126	Find the Result of 4 Times the 4x4 Identity Matrix	4	$4$ $4$
127	Find the Inverse	[[4,-10,29],[1,-2,5],[-3,7,-19]]	$⎡ ⎢ ⎣ \begin{matrix} 4 & - 10 & 29 1 & - 2 & 5 - 3 & 7 & - 19 \end{matrix} ⎤ ⎥ ⎦$ $[\begin{array}{c} 4 & - 10 & 29 \\ 1 & - 2 & 5 \\ - 3 & 7 & - 19 \end{array}]$
128	Solve the Matrix Equation	[[2x+3y],[3x-y]]=[[7],[16]]	$A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 7 8 & 2 6 & 6 \end{matrix} ⎤ ⎥ ⎦ B = [\begin{matrix} 4 & 6 7 & 2 \end{matrix}]$ $A = [\begin{array}{c} 2 & 7 \\ 8 & 2 \\ 6 & 6 \end{array}] B = [\begin{array}{c} 4 & 6 \\ 7 & 2 \end{array}]$
129	Find Pivot Positions and Pivot Columns	[[1,0,-5,0,-14],[0,1,2,0,-7],[0,0,0,1,7],[0,0,0,0,8]]	$⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 1 & 0 & - 5 & 0 & - 14 0 & 1 & 2 & 0 & - 7 0 & 0 & 0 & 1 & 7 0 & 0 & 0 & 0 & 8 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦$ $[\begin{array}{c} 1 & 0 & - 5 & 0 & - 14 \\ 0 & 1 & 2 & 0 & - 7 \\ 0 & 0 & 0 & 1 & 7 \\ 0 & 0 & 0 & 0 & 8 \end{array}]$
130	Solve Using an Inverse Matrix	3x+y=10 , 3x-2y=16	$3 x + y = 10$ $3 x + y = 10$ , $3 x - 2 y = 16$ $3 x - 2 y = 16$
131	Solve Using an Inverse Matrix	2y=-7x+3 , -7x-6y=5	$2 y = - 7 x + 3$ $2 y = - 7 x + 3$ , $- 7 x - 6 y = 5$ $- 7 x - 6 y = 5$
132	Solve Using an Inverse Matrix	-4x+9y=41 , 5x-4y=-44	$- 4 x + 9 y = 41$ $- 4 x + 9 y = 41$ , $5 x - 4 y = - 44$ $5 x - 4 y = - 44$
133	Solve Using an Inverse Matrix	4x-5y=22 , x+2y=-1	$4 x - 5 y = 22$ $4 x - 5 y = 22$ , $x + 2 y = - 1$ $x + 2 y = - 1$
134	Solve Using an Inverse Matrix	3x+y=-9 , 6x+2y=6	$3 x + y = - 9$ $3 x + y = - 9$ , $6 x + 2 y = 6$ $6 x + 2 y = 6$
135	Solve Using an Inverse Matrix	3y-5=x , x+y=115	$3 y - 5 = x$ $3 y - 5 = x$ , $x + y = 115$ $x + y = 115$
136	Solve Using an Inverse Matrix	2x+y=8 , 4x+2y=24	$2 x + y = 8$ $2 x + y = 8$ , $4 x + 2 y = 24$ $4 x + 2 y = 24$
137	Solve Using an Inverse Matrix	2x+y=8 , x+2y=1	$2 x + y = 8$ $2 x + y = 8$ , $x + 2 y = 1$ $x + 2 y = 1$
138	Solve Using an Inverse Matrix	3x-y-z=3 , -2x+3y+z=3 , 4x-2y-2z=2	$3 x - y - z = 3$ $3 x - y - z = 3$ , $- 2 x + 3 y + z = 3$ $- 2 x + 3 y + z = 3$ , $4 x - 2 y - 2 z = 2$ $4 x - 2 y - 2 z = 2$
139	Solve Using an Inverse Matrix	3y=11-2x , 3x=y-11	$3 y = 11 - 2 x$ $3 y = 11 - 2 x$ , $3 x = y - 11$ $3 x = y - 11$
140	Solve Using an Inverse Matrix	4r+7s=23 , r-2s=17	$4 r + 7 s = 23$ $4 r + 7 s = 23$ , $r - 2 s = 17$ $r - 2 s = 17$
141	Solve Using an Inverse Matrix	7x-5y=12 , 2x+3y=9	$7 x - 5 y = 12$ $7 x - 5 y = 12$ , $2 x + 3 y = 9$ $2 x + 3 y = 9$
142	Solve Using an Inverse Matrix	(2x+4y)=6 , (4x+8y)=0	$(2 x + 4 y) = 6$ $(2 x + 4 y) = 6$ , $(4 x + 8 y) = 0$ $(4 x + 8 y) = 0$
143	Solve Using an Inverse Matrix	y=x-5x+6 , y=x-2	$y = x - 5 x + 6$ $y = x - 5 x + 6$ , $y = x - 2$ $y = x - 2$
144	Solve Using an Inverse Matrix	x+4y=13 , 2x-y=-1	$x + 4 y = 13$ $x + 4 y = 13$ , $2 x - y = - 1$ $2 x - y = - 1$
145	Solve Using an Inverse Matrix	4x+3y=-2 , x-y=-4	$4 x + 3 y = - 2$ $4 x + 3 y = - 2$ , $x - y = - 4$ $x - y = - 4$
146	Solve Using an Inverse Matrix	x+2y-z=4 , 2x+y+z=-2 , x+2y+z=2	$x + 2 y - z = 4$ $x + 2 y - z = 4$ , $2 x + y + z = - 2$ $2 x + y + z = - 2$ , $x + 2 y + z = 2$ $x + 2 y + z = 2$
147	Solve Using an Inverse Matrix	x+3y=1 , x-y=6	$x + 3 y = 1$ $x + 3 y = 1$ , $x - y = 6$ $x - y = 6$
148	Solve Using an Inverse Matrix	x+3y=10 , 3x+9y=16	$x + 3 y = 10$ $x + 3 y = 10$ , $3 x + 9 y = 16$ $3 x + 9 y = 16$
149	Solve Using an Inverse Matrix	x+y+z=12 , 2x-3y+2z=4 , x+z=2y	$x + y + z = 12$ $x + y + z = 12$ , $2 x - 3 y + 2 z = 4$ $2 x - 3 y + 2 z = 4$ , $x + z = 2 y$ $x + z = 2 y$
150	Solve Using an Inverse Matrix	-7x-2y=-13 , x-2y=11	$- 7 x - 2 y = - 13$ $- 7 x - 2 y = - 13$ , $x - 2 y = 11$ $x - 2 y = 11$
151	Solve Using an Inverse Matrix	6x-y+3z=-13 , x+3y-z=-4 , 3x+3y-4z=3	$6 x - y + 3 z = - 13$ $6 x - y + 3 z = - 13$ , $x + 3 y - z = - 4$ $x + 3 y - z = - 4$ , $3 x + 3 y - 4 z = 3$ $3 x + 3 y - 4 z = 3$
152	Solve Using an Inverse Matrix	8x+6y=-4 , 9x-6y=-81	$8 x + 6 y = - 4$ $8 x + 6 y = - 4$ , $9 x - 6 y = - 81$ $9 x - 6 y = - 81$
153	Solve Using an Inverse Matrix	5x+4y=-2 , 3x-3y=2	$5 x + 4 y = - 2$ $5 x + 4 y = - 2$ , $3 x - 3 y = 2$ $3 x - 3 y = 2$
154	Solve Using an Inverse Matrix	-5x+y=7 , x+y=1	$- 5 x + y = 7$ $- 5 x + y = 7$ , $x + y = 1$ $x + y = 1$
155	Solve Using an Inverse Matrix	-5x+y=-8 , y=-4x+1	$- 5 x + y = - 8$ $- 5 x + y = - 8$ , $y = - 4 x + 1$ $y = - 4 x + 1$
156	Solve Using an Inverse Matrix	-5x-9Y=11 , 4x+5y=0	$- 5 x - 9 Y = 11$ $- 5 x - 9 Y = 11$ , $4 x + 5 y = 0$ $4 x + 5 y = 0$
157	Solve Using an Inverse Matrix	x=2y-5 , 2x-4y=-10	$x = 2 y - 5$ $x = 2 y - 5$ , $2 x - 4 y = - 10$ $2 x - 4 y = - 10$
158	Solve Using an Inverse Matrix	2x+4y=25 , x+5y=2	$2 x + 4 y = 25$ $2 x + 4 y = 25$ , $x + 5 y = 2$ $x + 5 y = 2$
159	Solve Using an Inverse Matrix	-2x+2y+3z=1 , x-y=3 , y+4z=-2	$- 2 x + 2 y + 3 z = 1$ $- 2 x + 2 y + 3 z = 1$ , $x - y = 3$ $x - y = 3$ , $y + 4 z = - 2$ $y + 4 z = - 2$
160	Solve Using an Inverse Matrix	2x+y=4 , -6x-3y=-12	$2 x + y = 4$ $2 x + y = 4$ , $- 6 x - 3 y = - 12$ $- 6 x - 3 y = - 12$
161	Solve Using an Inverse Matrix	y=6-2x , 7x-y=3	$y = 6 - 2 x$ $y = 6 - 2 x$ , $7 x - y = 3$ $7 x - y = 3$
162	Solve Using an Inverse Matrix	15x+11y=32 , 7y-9x=8	$15 x + 11 y = 32$ $15 x + 11 y = 32$ , $7 y - 9 x = 8$ $7 y - 9 x = 8$
163	Solve Using an Inverse Matrix	x=-3y+39 , 3x+4y=67	$x = - 3 y + 39$ $x = - 3 y + 39$ , $3 x + 4 y = 67$ $3 x + 4 y = 67$
164	Solve Using an Inverse Matrix	20=8y+11x , 11x+8y=79	$20 = 8 y + 11 x$ $20 = 8 y + 11 x$ , $11 x + 8 y = 79$ $11 x + 8 y = 79$
165	Solve Using an Inverse Matrix	2b+c+z=11 , 3b+4c+z=19 , 3b+6c+5z=43	$2 b + c + z = 11$ $2 b + c + z = 11$ , $3 b + 4 c + z = 19$ $3 b + 4 c + z = 19$ , $3 b + 6 c + 5 z = 43$ $3 b + 6 c + 5 z = 43$
166	Solve Using an Inverse Matrix	-(y-4)=x+9 , x-8/3y=0	$- (y - 4) = x + 9$ $- (y - 4) = x + 9$ , $x - \frac{8}{3} y = 0$ $x - \frac{8}{3} y = 0$
167	Solve Using an Inverse Matrix	2x+3y=-16 , 5x-10y=20	$2 x + 3 y = - 16$ $2 x + 3 y = - 16$ , $5 x - 10 y = 20$ $5 x - 10 y = 20$
168	Solve Using an Inverse Matrix	2x+3y=8 , 3x-y=1	$2 x + 3 y = 8$ $2 x + 3 y = 8$ , $3 x - y = 1$ $3 x - y = 1$
169	Solve Using an Inverse Matrix	2x+5y=1 , 4x+20y=6	$2 x + 5 y = 1$ $2 x + 5 y = 1$ , $4 x + 20 y = 6$ $4 x + 20 y = 6$
170	Solve Using an Inverse Matrix	2x+5y=1 , 6x+15y=3	$2 x + 5 y = 1$ $2 x + 5 y = 1$ , $6 x + 15 y = 3$ $6 x + 15 y = 3$
171	Solve Using an Inverse Matrix	-2x=27-5y , 4y=20+2x	$- 2 x = 27 - 5 y$ $- 2 x = 27 - 5 y$ , $4 y = 20 + 2 x$ $4 y = 20 + 2 x$
172	Solve Using an Inverse Matrix	2x-y=9 , 6x-3y=9	$2 x - y = 9$ $2 x - y = 9$ , $6 x - 3 y = 9$ $6 x - 3 y = 9$
173	Solve Using an Inverse Matrix	3x+5y=11 , x+3y=13	$3 x + 5 y = 11$ $3 x + 5 y = 11$ , $x + 3 y = 13$ $x + 3 y = 13$
174	Find the Adjoint	[[1,0,0],[0,2,6],[0,-4,-12]]	$⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 0 & 2 & 6 0 & - 4 & - 12 \end{matrix} ⎤ ⎥ ⎦$ $[\begin{array}{c} 1 & 0 & 0 \\ 0 & 2 & 6 \\ 0 & - 4 & - 12 \end{array}]$
175	Find the Cardinality	(-3,4)	$(- 3, 4)$ $(- 3, 4)$
176	Solve Using an Inverse Matrix	26a+8b=28 , 8a+3b=9	$26 a + 8 b = 28$ $26 a + 8 b = 28$ , $8 a + 3 b = 9$ $8 a + 3 b = 9$
177	Solve Using an Inverse Matrix	2x+2y=2 , 3x-y=1	$2 x + 2 y = 2$ $2 x + 2 y = 2$ , $3 x - y = 1$ $3 x - y = 1$
178	Solve Using an Inverse Matrix	2x+5y=-4 , 3x-y=11	$2 x + 5 y = - 4$ $2 x + 5 y = - 4$ , $3 x - y = 11$ $3 x - y = 11$
179	Solve Using an Inverse Matrix	x+y=-2 , x-2y=10	$x + y = - 2$ $x + y = - 2$ , $x - 2 y = 10$ $x - 2 y = 10$
180	Find the Domain	y-9=3/5x	$y - 9 = \frac{3}{5} x$ $y - 9 = \frac{3}{5} x$
181	Solve Using an Inverse Matrix	5y=x-1 , x-y=1	$5 y = x - 1$ $5 y = x - 1$ , $x - y = 1$ $x - y = 1$
182	Find the Cardinality	(2,0)	$(2, 0)$ $(2, 0)$
183	Find the Cardinality	B=(5,4,3,2,1,0)	$B = (5, 4, 3, 2, 1, 0)$ $B = (5, 4, 3, 2, 1, 0)$
184	Find the Cardinality	Q=(5,6,7,8)	$Q = (5, 6, 7, 8)$ $Q = (5, 6, 7, 8)$
185	Find the Cardinality	(0,5)	$(0, 5)$ $(0, 5)$
186	Find the Cardinality	(-2,3)	$(- 2, 3)$ $(- 2, 3)$
187	Find the Cardinality	(-3,7)	$(- 3, 7)$ $(- 3, 7)$
188	Find the Cardinality	(0,0)	$(0, 0)$ $(0, 0)$
189	Find the Power Set	Y=(3,6,8)	$Y = (3, 6, 8)$ $Y = (3, 6, 8)$
190	Find the Power Set	{1,2}	${1, 2}$ ${1, 2}$
191	Find the Power Set	A=(1,2,3,4)	$A = (1, 2, 3, 4)$ $A = (1, 2, 3, 4)$
192	Find the Power Set	A=(1,2,3,4,5,6)	$A = (1, 2, 3, 4, 5, 6)$ $A = (1, 2, 3, 4, 5, 6)$
193	Find the Cardinality	A=(4,6,8,9)	$A = (4, 6, 8, 9)$ $A = (4, 6, 8, 9)$
194	Find the Domain	y=-2x^2	$y = - 2 x^{2}$ $y = - 2 x^{2}$
195	Find the Adjoint	[[3,4,-1],[2,-2,3],[1,-1,x]]	$⎡ ⎢ ⎣ \begin{matrix} 3 & 4 & - 1 2 & - 2 & 3 1 & - 1 & x \end{matrix} ⎤ ⎥ ⎦$ $[\begin{array}{c} 3 & 4 & - 1 \\ 2 & - 2 & 3 \\ 1 & - 1 & x \end{array}]$
196	Evaluate	(2 square root of 3+ square root of 6)/(4 square root of 3- square root of 6)	$\frac{2 \sqrt{3 + \sqrt{6}}}{4 \sqrt{3 - \sqrt{6}}}$ $\frac{2 \sqrt{3 + \sqrt{6}}}{4 \sqrt{3 - \sqrt{6}}}$
197	Find the Cofactor Matrix	[[1,0,-2,2],[-3,-1,0,-3],[-3,-2,2,3],[-3,1,0,0]]	$⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 1 & 0 & - 2 & 2 - 3 & - 1 & 0 & - 3 - 3 & - 2 & 2 & 3 - 3 & 1 & 0 & 0 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦$ $[\begin{array}{c} 1 & 0 & - 2 & 2 \\ - 3 & - 1 & 0 & - 3 \\ - 3 & - 2 & 2 & 3 \\ - 3 & 1 & 0 & 0 \end{array}]$
198	Find the Cofactor Matrix	[[5,2],[4,3]]	$[\begin{matrix} 5 & 2 4 & 3 \end{matrix}]$ $[\begin{array}{c} 5 & 2 \\ 4 & 3 \end{array}]$
199	Find the Eigenvalues	[[1,-1,-2],[1,3,2],[1,-1,2]]	$⎡ ⎢ ⎣ \begin{matrix} 1 & - 1 & - 2 1 & 3 & 2 1 & - 1 & 2 \end{matrix} ⎤ ⎥ ⎦$ $[\begin{array}{c} 1 & - 1 & - 2 \\ 1 & 3 & 2 \\ 1 & - 1 & 2 \end{array}]$
200	Find Reduced Row Echelon Form	[[-6,5]]	$[\begin{matrix} - 6 & 5 \end{matrix}]$ $[\begin{array}{c} - 6 & 5 \end{array}]$