Chapter7: Systems Of Equations And Inequalities
Section7.7: Solving Systems With Inverses
Problem 4SE: Can a matrix with an entire column of zeros have an inverse? Explain why or why not.
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Question
![The image depicts a handwritten 3x3 matrix along with a notation indicating the calculation of its inverse. The matrix is shown as:
\[
\begin{bmatrix}
1 & 8 & 6 \\
4 & 5 & 7 \\
3 & 9 & 2 \\
\end{bmatrix}^{-1}
\]
The notation "-1" in the upper right corner signifies that the inverse of the matrix is being sought. Below this, space is provided to write the resulting inverse matrix once it is calculated. The inverse of a matrix is applicable only when the matrix is square and its determinant is non-zero. Calculating the inverse involves several steps including finding the determinant, the matrix of minors, the cofactor matrix, the adjugate, and then dividing by the determinant.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F80321e65-f5af-4407-990e-2a73bdb503ea%2Fcf0e7490-3423-4fc5-a0d4-11ce1a5c1847%2Fbye6p1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image depicts a handwritten 3x3 matrix along with a notation indicating the calculation of its inverse. The matrix is shown as:
\[
\begin{bmatrix}
1 & 8 & 6 \\
4 & 5 & 7 \\
3 & 9 & 2 \\
\end{bmatrix}^{-1}
\]
The notation "-1" in the upper right corner signifies that the inverse of the matrix is being sought. Below this, space is provided to write the resulting inverse matrix once it is calculated. The inverse of a matrix is applicable only when the matrix is square and its determinant is non-zero. Calculating the inverse involves several steps including finding the determinant, the matrix of minors, the cofactor matrix, the adjugate, and then dividing by the determinant.
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