Solve the system of equations using matrices: { 7 x + 5 y = 3 3 x − 2 y = 22. 7 x + 5 y = 3 3 x − 2 y = 22 → [ 7 x + 5 y 3 x − 2 y] = [ 3 22] Write the matrix on the left as the product of coefficients

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5x - 2y = 7. Now, the coefficient matrix is, A = ⎡ ⎢⎣−3 2 5 −2 ⎤ ⎥⎦ [ − 3 2 5 − 2]. The variable matrix is, X = ⎡ ⎢⎣x y ⎤ ⎥⎦ [ x y]. The constant matrix is, B = ⎡ ⎢⎣−2 7 ⎤ ⎥⎦ [ − 2 7]. Thus, the matrix equation is:

Solve the system of equations using a matrix: { x − 2 y + 3 z = 1 x + y − 3 z = 7 3 x − 4 y + 5 z = 7. Write the augmented matrix for the equations. The entry in row 1, column 1 is 1. Using row

\begin{pmatrix}4&0\\6&-2\\3&1\end{pmatrix}=\begin{pmatrix}x&0\\6&y+4\\\frac{z}{3}&1\end{pmatrix}

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