Use Matrices to Represent Systems of Linear Equations
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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
- Using Matrices to Represent Systems of Linear Equations When we learned about elementary row operations in earlier lessons, we talked about using them later. Well, this is that …
By Anusha Rahman
Problems 10
- What equations are given by this matrix? [123∣4234∣5345∣6]\begin{bmatrix} 1&2&3&|&4\\ 2&3&4&|&5\\ 3&4&5&|&6 \end{bmatrix}123234345∣∣∣456
- 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{…
- Convert the system of equations into its equivalent augmented matrix. {2x+3y=64x−2y=9\begin{cases}2x+3y=6\\4x-2y=9\end{cases}{2x+3y=64x−2y=9
- Convert the system of equations into its equivalent augmented matrix. {15x+5y+8z=137x−6y−3=124x+8y+12z=56\begin{cases}15x+5y+8z=13\\7x-6y-3=12\\4x+8y+12z=56\end{cases}⎩⎨⎧15x+5y…
- Convert the system of equations into its equivalent augmented matrix. {12x−9z+y=07z−18+6y=123x+9z+4w=7\begin{cases}12x-9z+y=0\\7z-18+6y=12\\3x+9z+4w=7\end{cases}⎩⎨⎧12x−9z+y=07z…
- Let aaa, bbb, ccc, xxx, yyy, and zzz be real numbers that satisfy the three equations 13x+by+cz=0ax+23y+cz=0ax+by+42z=0.\begin{align*} 13x + by + cz &= 0 \\ ax + 23y + cz &= 0 \…
- Use a matrix to solve this system and find out how many toys, treats, and walks are needed to spoil your dog.