Question

Use the given inverse of the coefficient matrix to solve the following system 5x_1+3x_2=6 -6x_1-3x_2=-2 A^{-1}=\begin{bmatrix}-1 & -1 \\2 & \frac{5}{3} \end{bmatrix}

Matrix transformations
ANSWERED
asked 2021-05-19
Use the given inverse of the coefficient matrix to solve the following system
\(5x_1+3x_2=6\)
\(-6x_1-3x_2=-2\)
\(A^{-1}=\begin{bmatrix}-1 & -1 \\2 & \frac{5}{3} \end{bmatrix}\)

Expert Answers (2)

2021-05-20
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8
 
Best answer
2021-09-09

\(Ax=B\)

\(x=A^{-1}B\)

\(\left(\begin{array}{c}x_1\\ x_2\end{array}\right)=\left(\begin{array}{c}-1&-1\\ 2&\frac{5}{3}\end{array}\right)\left(\begin{array}{c}6\\-2\end{array}\right)\)

\(=\left(\begin{array}{c}(-1)(6)+(-1)(-2)\\(2)(6)+(\frac{5}{3})(-2)\end{array}\right)\)

\(\left(\begin{array}{c}x_1\\x_2\end{array}\right)=\left(\begin{array}{c}-6+2\\ 12-\frac{10}{3}\end{array}\right)\)

\(=\left(\begin{array}{c}-4\\\frac{26}{3}\end{array}\right)\)

So, \(x_1=-4\ x_2=\frac{26}{3}\)

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