Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
901	Multiply the Matrices	[[4,6,1],[5,3,1],[3,3,1]][[3,2],[3,4],[2,2]]	$[\begin{array}{c} 4 & 6 & 1 \\ 5 & 3 & 1 \\ 3 & 3 & 1 \end{array}] [\begin{array}{c} 3 & 2 \\ 3 & 4 \\ 2 & 2 \end{array}]$
902	Multiply the Matrices	[[5,2],[7,6],[1,0]][[1,4,0],[2,-1,2]]	$[\begin{array}{c} 5 & 2 \\ 7 & 6 \\ 1 & 0 \end{array}] [\begin{array}{c} 1 & 4 & 0 \\ 2 & - 1 & 2 \end{array}]$
903	Solve Using a Matrix with Cramer's Rule	2x-5y=10 , 4x-10y=20	$2 x - 5 y = 10$ , $4 x - 10 y = 20$
904	Solve Using a Matrix with Cramer's Rule	2x+5y-2z=14 , 5x-6y+2z=0 , 4x-y+3z=-7	$2 x + 5 y - 2 z = 14$ , $5 x - 6 y + 2 z = 0$ , $4 x - y + 3 z = - 7$
905	Solve Using a Matrix with Cramer's Rule	-3x1+5x2=-9 , -4x1+4x3=20 , 2x1+x2+2x*3=-1	$- 3 x \cdot 1 + 5 x \cdot 2 = - 9$ , $- 4 x \cdot 1 + 4 x \cdot 3 = 20$ , $2 x \cdot 1 + x \cdot 2 + 2 x \cdot 3 = - 1$
906	Solve Using a Matrix with Cramer's Rule	5x-3y+4z=7 , 5x+2y-2z=11 , 20x-7y+10z=32	$5 x - 3 y + 4 z = 7$ , $5 x + 2 y - 2 z = 11$ , $20 x - 7 y + 10 z = 32$
907	Solve Using a Matrix with Cramer's Rule	9y-5x=3 , x+y=1 , z+2y=2	$9 y - 5 x = 3$ , $x + y = 1$ , $z + 2 y = 2$
908	Solve Using a Matrix with Cramer's Rule	x+4y+5z=18 , z=-7	$x + 4 y + 5 z = 18$ , $z = - 7$
909	Solve Using a Matrix with Cramer's Rule	x+y+z=7 , x-y+2z=7 , 2x+3z=15	$x + y + z = 7$ , $x - y + 2 z = 7$ , $2 x + 3 z = 15$
910	Solve by Substitution	yint=1 , xint=-8
911	Solve by Substitution	12x-5y=9 , 3x-8y=-18	$12 x - 5 y = 9$ , $3 x - 8 y = - 18$
912	Solve by Substitution	2x-8y=3 , -16x+64y=-23	$2 x - 8 y = 3$ , $- 16 x + 64 y = - 23$
913	Solve by Substitution	2x+y=7 , x-y=3	$2 x + y = 7$ , $x - y = 3$
914	Solve by Substitution	2x-5y=10 , 4x-10y=20	$2 x - 5 y = 10$ , $4 x - 10 y = 20$
915	Solve by Substitution	3x-2y=-3 , 5x-y=2	$3 x - 2 y = - 3$ , $5 x - y = 2$
916	Solve by Substitution	3x-2y=7 , 9x-6y=14	$3 x - 2 y = 7$ , $9 x - 6 y = 14$
917	Solve by Substitution	5x+2y-4=0 , 3x-y-9=0	$5 x + 2 y - 4 = 0$ , $3 x - y - 9 = 0$
918	Solve by Substitution	x+3y+z=76 , 7y+2z=28	$x + 3 y + z = 76$ , $7 y + 2 z = 28$
919	Solve by Substitution	x-2y=-2 , 6x-3y=-30	$x - 2 y = - 2$ , $6 x - 3 y = - 30$
920	Solve by Substitution	5x-6y=8 , 10x-12y=16	$5 x - 6 y = 8$ , $10 x - 12 y = 16$
921	Solve by Substitution	2x-5y=10 , 6x-15y=30	$2 x - 5 y = 10$ , $6 x - 15 y = 30$
922	Solve by Substitution	5/4x-2/3y=3 , 1/4x+5/3y=6	$\frac{5}{4} x - \frac{2}{3} y = 3$ , $\frac{1}{4} x + \frac{5}{3} y = 6$
923	Solve by Substitution	5y+4x=0 , 4x+3y=-6/5	$5 y + 4 x = 0$ , $4 x + 3 y = - \frac{6}{5}$
924	Solve by Substitution	4x+y=3 , 3x+y=4	$4 x + y = 3$ , $3 x + y = 4$
925	Solve by Substitution	4x-y+9z=92 , 3x+3y+3z=54 , -7x-7y+z=-62	$4 x - y + 9 z = 92$ , $3 x + 3 y + 3 z = 54$ , $- 7 x - 7 y + z = - 62$
926	Solve by Substitution	3x-2y=12 , 6x-4y=-24	$3 x - 2 y = 12$ , $6 x - 4 y = - 24$
927	Solve by Substitution	3x-9y=21 , -2x+6y=-14	$3 x - 9 y = 21$ , $- 2 x + 6 y = - 14$
928	Solve by Substitution	2x-5y=21 , 3x+7y=-12	$2 x - 5 y = 21$ , $3 x + 7 y = - 12$
929	Solve by Substitution	x=-3y , 2x-3y=9	$x = - 3 y$ , $2 x - 3 y = 9$
930	Solve by Substitution	x=y+3 , x-2y=5	$x = y + 3$ , $x - 2 y = 5$
931	Solve by Substitution	x+3y+6z=20 , 2x-3y+3z=4	$x + 3 y + 6 z = 20$ , $2 x - 3 y + 3 z = 4$
932	Solve by Substitution	-x-2y=-4 , x+2y=4	$- x - 2 y = - 4$ , $x + 2 y = 4$
933	Solve by Substitution	x-2y=8 , 3x+4y=4	$x - 2 y = 8$ , $3 x + 4 y = 4$
934	Solve by Substitution	x-y+3z=13 , 4x+y+2z=17 , 3x+2y+2z=1	$x - y + 3 z = 13$ , $4 x + y + 2 z = 17$ , $3 x + 2 y + 2 z = 1$
935	Solve by Substitution	-8x+2y=8 , 4x-y=0	$- 8 x + 2 y = 8$ , $4 x - y = 0$
936	Find the Intersection of the Inequalities	3x+y=-6 , x-y=3	$3 x + y = - 6$ , $x - y = 3$
937	Find the Intersection of the Inequalities	2x+3y=12 , x=0 , y=0	$2 x + 3 y = 12$ , $x = 0$ , $y = 0$
938	Find the Intersection of the Inequalities	x+3y=6 , 4x+5y=20	$x + 3 y = 6$ , $4 x + 5 y = 20$
939	Find the Intersection of the Inequalities	3x-2y=6 , x+y=2	$3 x - 2 y = 6$ , $x + y = 2$
940	Minimize the Equation given the Constraints	z=4x+7y , x-y=1 , 3x+2y=18 , x=0 , y=0	$z = 4 x + 7 y$ , $x - y = 1$ , $3 x + 2 y = 18$ , $x = 0$ , $y = 0$
941	Find the Intersection of the Inequalities	2x+y=10 , x+y=7 , x+2y=12	$2 x + y = 10$ , $x + y = 7$ , $x + 2 y = 12$
942	Find the Intersection of the Inequalities	2x-5y=10 , x+y=2	$2 x - 5 y = 10$ , $x + y = 2$
943	Find the Intersection of the Inequalities	x+y=6 , -x+y=2 , 2x-y=8	$x + y = 6$ , $- x + y = 2$ , $2 x - y = 8$
944	Find the Intersection of the Inequalities	x+2y=2 , x-y=0	$x + 2 y = 2$ , $x - y = 0$
945	Find the Intersection of the Inequalities	x-4y=-8 , 3x+y=6	$x - 4 y = - 8$ , $3 x + y = 6$
946	Solve Using a Matrix with Cramer's Rule	x+y-z=0 , x-y+z=8 , x+5y-z=-20	$x + y - z = 0$ , $x - y + z = 8$ , $x + 5 y - z = - 20$
947	Maximize the Equation given the Constraints	0=z-9x1-8x2 , x1+2x2=2 , 3x1+2x2=8 , 2x1+3x2=10	$0 = z - 9 x \cdot 1 - 8 x \cdot 2$ , $x \cdot 1 + 2 x \cdot 2 = 2$ , $3 x \cdot 1 + 2 x \cdot 2 = 8$ , $2 x \cdot 1 + 3 x \cdot 2 = 10$
948	Maximize the Equation given the Constraints	0.09x+0.14y=40 , x=0.12	$0.09 x + 0.14 y = 40$ , $x = 0.12$
949	Maximize the Equation given the Constraints	p=20x+12y+18z , 3x+y+2z=9 , 2x+3y+z=8 , x+2y+3z=7	$p = 20 x + 12 y + 18 z$ , $3 x + y + 2 z = 9$ , $2 x + 3 y + z = 8$ , $x + 2 y + 3 z = 7$
950	Solve Using a Matrix with Cramer's Rule	x+2y=4 , 2x+6y=5	$x + 2 y = 4$ , $2 x + 6 y = 5$
951	Maximize the Equation given the Constraints	p=3x+4y , x+y=4 , 2x+y=6	$p = 3 x + 4 y$ , $x + y = 4$ , $2 x + y = 6$
952	Maximize the Equation given the Constraints	z=4x+8y , x-y=1 , 3x+2y=18 , x=0 , y=0	$z = 4 x + 8 y$ , $x - y = 1$ , $3 x + 2 y = 18$ , $x = 0$ , $y = 0$
953	Minimize the Equation given the Constraints	p=5x+8y+7z , x+y+z=6 , 5x+5y+3z=22	$p = 5 x + 8 y + 7 z$ , $x + y + z = 6$ , $5 x + 5 y + 3 z = 22$
954	Maximize the Equation given the Constraints	z=3x+5y , x=4 , 2y=12 , 3x+2y=18	$z = 3 x + 5 y$ , $x = 4$ , $2 y = 12$ , $3 x + 2 y = 18$
955	Maximize the Equation given the Constraints	z=8x+7y , 4x+3y=24 , 3x+4y=8 , x , y=0	$z = 8 x + 7 y$ , $4 x + 3 y = 24$ , $3 x + 4 y = 8$ , $x$ , $y = 0$
956	Minimize the Equation given the Constraints	c=4x+5y , x+2y=10 , 2x+3y=18	$c = 4 x + 5 y$ , $x + 2 y = 10$ , $2 x + 3 y = 18$
957	Minimize the Equation given the Constraints	z=2x+8y , x-y=-1 , 3x+2y=12 , x=0 , y=0	$z = 2 x + 8 y$ , $x - y = - 1$ , $3 x + 2 y = 12$ , $x = 0$ , $y = 0$
958	Find the Equation with Real Coefficients	x+5y-9z=-8 , z=-3	$x + 5 y - 9 z = - 8$ , $z = - 3$
959	Find the Equation with Real Coefficients	x+2y+3z=90 , 3y+4z=36	$x + 2 y + 3 z = 90$ , $3 y + 4 z = 36$
960	Find the Equation with Real Coefficients	x+2y+3z=90 , 3y+z=36	$x + 2 y + 3 z = 90$ , $3 y + z = 36$
961	Find the Intersection of the Inequalities	x+y=4 , x-y=6	$x + y = 4$ , $x - y = 6$
962	Solve in Terms of the Arbitrary Variable z	2x+5y-z=2 , 3x+8y+z=5	$2 x + 5 y - z = 2$ , $3 x + 8 y + z = 5$
963	Solve in Terms of the Arbitrary Variable z	6x+6y+z=60 , 3x+4y+z=42	$6 x + 6 y + z = 60$ , $3 x + 4 y + z = 42$
964	Find the Quadrant	(12,8)	$p (12, 8)$
965	Find the Equation Using Two Points	(4,1) , (1,3)	$(4, 1)$ , $(1, 3)$
966	Find the Slope	(2,3) , (-3,1)	$(2, 3) (- 3, 1)$
967	Multiply the Matrices	[[1/3,1/6,-1/6]][[4],[-18],[8]]	$[\begin{array}{c} \frac{1}{3} & \frac{1}{6} & - \frac{1}{6} \end{array}] [\begin{array}{c} 4 \\ - 18 \\ 8 \end{array}]$
968	Find the Inverse	[[0.9,-0.4],[-0.45,0.8]]	$[\begin{array}{c} 0.9 & - 0.4 \\ - 0.45 & 0.8 \end{array}]$
969	Find the Inverse	[[1,0,5],[0,1,-10],[0,0,5]]	$[\begin{array}{c} 1 & 0 & 5 \\ 0 & 1 & - 10 \\ 0 & 0 & 5 \end{array}]$
970	Find the Inverse	[[-1,-1,0],[-1,2,1],[-2,-2,1]]	$[\begin{array}{c} - 1 & - 1 & 0 \\ - 1 & 2 & 1 \\ - 2 & - 2 & 1 \end{array}]$
971	Find the Inverse	[[-1,-2],[3,6]]	$[\begin{array}{c} - 1 & - 2 \\ 3 & 6 \end{array}]$
972	Solve Using a Matrix by Row Operations	3x-2y=7 , 9x-6y=14	$3 x - 2 y = 7$ , $9 x - 6 y = 14$
973	Find the Inverse	[[1,1,1],[1,-1,3],[5,1,1]]	$[\begin{array}{c} 1 & 1 & 1 \\ 1 & - 1 & 3 \\ 5 & 1 & 1 \end{array}]$
974	Find the Inverse	[[1,2],[1,3]]	$[\begin{array}{c} 1 & 2 \\ 1 & 3 \end{array}]$
975	Find the Inverse	[[2,0,-1],[0,-1,0],[3,-2,-2]]	$[\begin{array}{c} 2 & 0 & - 1 \\ 0 & - 1 & 0 \\ 3 & - 2 & - 2 \end{array}]$
976	Find the Inverse	A=[[0,1,-1],[2,-2,-1],[-1,1,1]]	$A = [\begin{array}{c} 0 & 1 & - 1 \\ 2 & - 2 & - 1 \\ - 1 & 1 & 1 \end{array}]$
977	Find the Determinant	[[-3,2,-1],[8,0,2],[-12,6,-3]]	$[\begin{array}{c} - 3 & 2 & - 1 \\ 8 & 0 & 2 \\ - 12 & 6 & - 3 \end{array}]$
978	Find the Determinant	[[4.72,6.68],[3.64,3.65]]	$[\begin{array}{c} 4.72 & 6.68 \\ 3.64 & 3.65 \end{array}]$
979	Find the Inverse	[[0.5,0.5],[0.6,0.4]]	$[\begin{array}{c} 0.5 & 0.5 \\ 0.6 & 0.4 \end{array}]$
980	Simplify the Matrix	[[5,3]][[4],[7]]	$[\begin{array}{c} 5 & 3 \end{array}] [\begin{array}{c} 4 \\ 7 \end{array}]$
981	Simplify the Matrix	[[-1,0],[0,1]][[0,5,5,1,1,0],[0,0,1,1,8,8]]	$[\begin{array}{c} - 1 & 0 \\ 0 & 1 \end{array}] [\begin{array}{c} 0 & 5 & 5 & 1 & 1 & 0 \\ 0 & 0 & 1 & 1 & 8 & 8 \end{array}]$
982	Simplify the Matrix	[[-4,0],[20,36]]-[[-18,-16],[-2,-10]]	$[\begin{array}{c} - 4 & 0 \\ 20 & 36 \end{array}] - [\begin{array}{c} - 18 & - 16 \\ - 2 & - 10 \end{array}]$
983	Simplify the Matrix	[[4,6,1],[5,3,1],[3,3,1]]*[[3,2],[3,4],[2,2]]	$[\begin{array}{c} 4 & 6 & 1 \\ 5 & 3 & 1 \\ 3 & 3 & 1 \end{array}] \cdot [\begin{array}{c} 3 & 2 \\ 3 & 4 \\ 2 & 2 \end{array}]$
984	Find the Determinant	[[1,-2,1],[2,-5,1],[1,6,3]]	$[\begin{array}{c} 1 & - 2 & 1 \\ 2 & - 5 & 1 \\ 1 & 6 & 3 \end{array}]$
985	Find the Determinant	[[1,3],[2,-3]]	$[\begin{array}{c} 1 & 3 \\ 2 & - 3 \end{array}]$
986	Simplify the Matrix	[[0,1,0],[0.8,0,0.2],[1,0,0]][[0,1,0],[0.8,0,0.2],[1,0,0]]	$[\begin{array}{c} 0 & 1 & 0 \\ 0.8 & 0 & 0.2 \\ 1 & 0 & 0 \end{array}] [\begin{array}{c} 0 & 1 & 0 \\ 0.8 & 0 & 0.2 \\ 1 & 0 & 0 \end{array}]$
987	Simplify the Matrix	-4[[1,-1],[0,2],[0,-2]]	$- 4 [\begin{array}{c} 1 & - 1 \\ 0 & 2 \\ 0 & - 2 \end{array}]$
988	Simplify the Matrix	2[[0,0],[8,-1]]	$2 [\begin{array}{c} 0 & 0 \\ 8 & - 1 \end{array}]$
989	Simplify the Matrix	[[1,-1,3,16],[3,0,1,4],[1,2,1,-4]]	$[\begin{array}{c} 1 & - 1 & 3 & 16 \\ 3 & 0 & 1 & 4 \\ 1 & 2 & 1 & - 4 \end{array}]$
990	Simplify the Matrix	[[2,-1],[0,1]][[2,-1],[-1,-1]]	$[\begin{array}{c} 2 & - 1 \\ 0 & 1 \end{array}] [\begin{array}{c} 2 & - 1 \\ - 1 & - 1 \end{array}]$
991	Simplify the Matrix	[[1,-2,2],[0,2,-2]][[-3,0,1],[4,-1,1],[-3,3,1]][[1,-1],[0,-2],[3,3]]	$[\begin{array}{c} 1 & - 2 & 2 \\ 0 & 2 & - 2 \end{array}] [\begin{array}{c} - 3 & 0 & 1 \\ 4 & - 1 & 1 \\ - 3 & 3 & 1 \end{array}] [\begin{array}{c} 1 & - 1 \\ 0 & - 2 \\ 3 & 3 \end{array}]$
992	Simplify the Matrix	[[4+8i,i],[i,10+5i]]	$[\begin{array}{c} 4 + 8 i & i \\ i & 10 + 5 i \end{array}]$
993	Simplify the Matrix	[[-16,16],[18,0],[-10,6]]-[[-6,-2],[-4,-2],[12,6]]	$[\begin{array}{c} - 16 & 16 \\ 18 & 0 \\ - 10 & 6 \end{array}] - [\begin{array}{c} - 6 & - 2 \\ - 4 & - 2 \\ 12 & 6 \end{array}]$
994	Simplify the Matrix	[[6,2,-8,4]]	$[\begin{array}{c} 6 & 2 & - 8 & 4 \end{array}]$
995	Simplify the Matrix	[[8,0,5,1,1,0,0,29],[7,1,5,0,1,0,0,18],[2,0,8,0,2,0,1,60]]	$[\begin{array}{c} 8 & 0 & 5 & 1 & 1 & 0 & 0 & 29 \\ 7 & 1 & 5 & 0 & 1 & 0 & 0 & 18 \\ 2 & 0 & 8 & 0 & 2 & 0 & 1 & 60 \end{array}]$
996	Simplify the Matrix	[[-1,3],[5,4]][[0,-2,4],[1,-3,2]]	$[\begin{array}{c} - 1 & 3 \\ 5 & 4 \end{array}] [\begin{array}{c} 0 & - 2 & 4 \\ 1 & - 3 & 2 \end{array}]$
997	Find Reduced Row Echelon Form	[[1,-5,4],[2,2,5]]	$[\begin{array}{c} 1 & - 5 & 4 \\ 2 & 2 & 5 \end{array}]$
998	Find Reduced Row Echelon Form	[[1,1,4],[1,-1,2]]	$[\begin{array}{c} 1 & 1 & 4 \\ 1 & - 1 & 2 \end{array}]$
999	Find Reduced Row Echelon Form	[[2,3,4],[3,4,3]]	$[\begin{array}{c} 2 & 3 & 4 \\ 3 & 4 & 3 \end{array}]$
1000	Find Reduced Row Echelon Form	[[1,3,2,-10],[0,1,2,-3]]	$[\begin{array}{c} 1 & 3 & 2 & - 10 \\ 0 & 1 & 2 & - 3 \end{array}]$