Use Matrices to Solve Systems of Three or More Variables
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- Let's say we have the system of equations: {x+y+z=62y+5z=−42x+5y−z=27\begin{cases} x + y + z &= 6 \\ 2y + 5z &= -4 \\ 2x + 5y - z &= 27 \\ \end{cases}⎩⎨⎧x+y+z2y+5z2x+5y−z=6=−4…
By Nisha Devasia, Catherine Yeo, Moor Xu, Gabi Slizewska, Anusha Rahman
- (Video) How to Write an Augmented Matrix by IntFinder Here's a video by IntFinder on how you write a system of equations as an augmented matrix. An augmented matrix is just a ma…
By Alex Federspiel, Anusha Rahman
Problems 7
- Solve the following system of equations in matrix form. [42−1−132−413][xyz]=[147−5]\begin{bmatrix} 4 & 2 & -1 \\ -1 & 3 & 2 \\ -4 & 1 & 3 \end{bmatrix} \begin{bmatrix} x \\ y \\…
- Solve the following system of equations in matrix form. [34−12−201−81][xyz]=[345]\begin{bmatrix} 3 & 4 & -1 \\ 2 & -2 & 0 \\ 1 & -8 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \\ z…
- Let AAA be a 3×33 \times 33×3 matrix and assume, for constants b1,b2,b3b_1, b_2, b_3b1,b2,b3: A[xyz]=[b1b2b3]A \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} b_1…
- [−132−4571−10−3][xyz]=[415b]\begin{bmatrix} -1 & 3 & 2 \\ -4 & 5 & 7 \\ 1 & -10 & -3 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 4 \\ 15 \\ b \end{…
- Solve this system of equations using matrix methods. {−4x+2y−6z=−568x+2y−3z= 16−2x−8y−7z=−96\\\begin{cases}-4x+2y-6z&=-56\\8x+2y-3z&=\ \ \ 16\\-2x-8y-7z&=-96\end{cases}⎩⎨⎧−4x+2…
- Solve this system of equations using matrix methods. {−7x+4y−4z=−122−8y−6z=347x−6y+10z=168\\\begin{cases}-7x+4y-4z&=-122\\-8y-6z&=34\\7x-6y+10z&=168\end{cases}⎩⎨⎧−7x+4y−4z−8y−6…
- Solve. [−16−1982−10−224−4−5−16]\\\left[\begin{array}{ccc|c}-1&6&-1&9\\8&2&-10&-22\\4&-4&-5&-16\end{array}\right]−18462−4−1−10−59−22−16