Chadwick Mccarthy
07/03/2023 · Middle School
Solve the matrix equation \( A X=B \) for \( X \) \( A=\left[\begin{array}{cc}0 & -1 \\ 1 & 4\end{array}\right], B=\left[\begin{array}{c}-5 \\ 18\end{array}\right] \) \( X= \)
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Tutor-Verified Answer
Step-by-step Solution
Solve the matrix equation \( 0X_{11}-1X_{12}=-5;1X_{11}+4X_{12}=18 \).
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}0\times X_{11}-1\times X_{12}=-5\\1\times X_{11}+4X_{12}=18\end{array}\right.\)
- step1: Calculate:
\(\left\{ \begin{array}{l}-X_{12}=-5\\X_{11}+4X_{12}=18\end{array}\right.\)
- step2: Solve the equation:
\(\left\{ \begin{array}{l}X_{12}=5\\X_{11}+4X_{12}=18\end{array}\right.\)
- step3: Substitute the value of \(X_{12}:\)
\(X_{11}+4\times 5=18\)
- step4: Simplify:
\(X_{11}+20=18\)
- step5: Move the constant to the right side:
\(X_{11}=18-20\)
- step6: Subtract the numbers:
\(X_{11}=-2\)
- step7: Calculate:
\(\left\{ \begin{array}{l}X_{11}=-2\\X_{12}=5\end{array}\right.\)
- step8: Check the solution:
\(\left\{ \begin{array}{l}X_{11}=-2\\X_{12}=5\end{array}\right.\)
- step9: Rewrite:
\(\left(X_{11},X_{12}\right) = \left(-2,5\right)\)
The solution to the matrix equation \( A X=B \) is \( X = \begin{bmatrix} -2 \\ 5 \end{bmatrix} \).
Quick Answer
\( X = \begin{bmatrix} -2 \\ 5 \end{bmatrix} \)
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