Solve the matrix equation AX = B for X. 1-2-3 HH - 1 4 6 B= 6 1 -1 -2 A = 3 7
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.5: Determinants
Problem 72E
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![**Solve the Matrix Equation**
We are tasked with solving the matrix equation \(AX = B\) for \(X\).
**Matrix A:**
\[
A = \begin{bmatrix}
1 & -2 & -3 \\
-1 & 4 & 6 \\
1 & -1 & -2
\end{bmatrix}
\]
**Matrix B:**
\[
B = \begin{bmatrix}
3 \\
6 \\
7
\end{bmatrix}
\]
**Matrix X:**
\[
X = \begin{bmatrix}
\Box \\
\Box \\
\Box
\end{bmatrix}
\]
To find \(X\), we need to solve the system of linear equations represented by the matrix equation \(AX = B\). This involves finding the inverse of matrix \(A\) if it exists, and then calculating \(X = A^{-1}B\).
Follow these steps to solve the equation:
1. **Check if the determinant of \(A\) is non-zero to ensure the inverse exists.**
2. **Calculate the inverse \(A^{-1}\).**
3. **Multiply \(A^{-1}\) by \(B\) to find \(X\).**
Enter the values of \(X\) in the boxes provided after calculating.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c391909-e4e2-4c58-85bb-5bea7cb900f2%2F202c54fb-71c5-4720-ab29-2a268d472ab3%2Fvs4vc2r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solve the Matrix Equation**
We are tasked with solving the matrix equation \(AX = B\) for \(X\).
**Matrix A:**
\[
A = \begin{bmatrix}
1 & -2 & -3 \\
-1 & 4 & 6 \\
1 & -1 & -2
\end{bmatrix}
\]
**Matrix B:**
\[
B = \begin{bmatrix}
3 \\
6 \\
7
\end{bmatrix}
\]
**Matrix X:**
\[
X = \begin{bmatrix}
\Box \\
\Box \\
\Box
\end{bmatrix}
\]
To find \(X\), we need to solve the system of linear equations represented by the matrix equation \(AX = B\). This involves finding the inverse of matrix \(A\) if it exists, and then calculating \(X = A^{-1}B\).
Follow these steps to solve the equation:
1. **Check if the determinant of \(A\) is non-zero to ensure the inverse exists.**
2. **Calculate the inverse \(A^{-1}\).**
3. **Multiply \(A^{-1}\) by \(B\) to find \(X\).**
Enter the values of \(X\) in the boxes provided after calculating.
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