Solve Systems Using an Inverse Matrix
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- Matrices and Systems Let's say you're in algebra and you're given a system of equations. You could certainly use substitution or graphing to solve it, but there is an even coole…
By Clare Burhenne, Karen Ying, Laurence Putterman, Gabi Slizewska, Anusha Rahman
- (Video) Cramer's Rule by patrickJMT In this video, patrickJMT walks you through the proof for Cramer's Rule. Summary Cramer's Rule is a way to solve a system of linear equations…
By Neil Chowdhury, Anusha Rahman
- While solving systems of equations through direct methods (like substitution, graphing, and elimination) is often quicker, sometimes you'll be asked to use a matrix. Or, maybe y…
By Hannah Bonville, Zora Gilbert, Alex Federspiel, Gabi Slizewska, Anusha Rahman
- Solving Systems Using an Inverse Matrix Now that we understand that we can use matrices to solve systems of linear equations, we will learn how to use the inverse matrix specifi…
By Anusha Rahman
Problems 8
- Solve this system of linear equations using the inverse. {5x+y=133x+2y=5\begin{cases}5x+y=13\\3x+2y=5\end{cases}{5x+y=133x+2y=5
- Solve this system of linear equations using the inverse. {8x+3y=382y−7x=−24\begin{cases}8x+3y=38\\2y-7x=-24\end{cases}{8x+3y=382y−7x=−24
- Solve this system of linear equations using the inverse. {3x+5y=77x−13y=4\begin{cases}3x+5y=7\\7x-13y=4\end{cases}{3x+5y=77x−13y=4
- Solve this system of linear equations using the inverse. {2x+7y+z=24−3x−2y+5z=−196x+3y+3z=36\begin{cases}2x+7y+z=24\\-3x-2y+5z=-19\\6x+3y+3z=36\end{cases}⎩⎨⎧2x+7y+z=24−3x−2y+5z…
- Solve this system of linear equations using the inverse. {9x+2y+8z=1677x−9y+5z=139y+4z=133\begin{cases}9x+2y+8z&=167\\7x-9y+5z&=13\\9y+4z&=133\end{cases}⎩⎨⎧9x+2y+8z7x−9y+5z9y+4…
- Solve this system of linear equations using the inverse. {2x−y+9z=102x+y+4z=114x+6y−3z=23\begin{cases}2x-y+9z&=10\\2x+y+4z&=11\\4x+6y-3z&=23\end{cases}⎩⎨⎧2x−y+9z2x+y+4z4x+6y−3z…
- Solve. [810104611087][xyz]=[28−1838]\\\begin{bmatrix}8&10&10\\4&6&1\\10&8&7\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}28\\-18\\38\end{bmatrix}84101068101…
- Solve this system of linear equations using the inverse. {ax+by=3b2c +dcx+dy=d(3ab+c2)ac\begin{cases}ax+by&=3\frac{b^2}{c}\ +d\\cx+dy&=\frac{d(3ab+c^2)}{ac}\end{cases}{ax+bycx+d…