SECTION 2.4 PROBLEM SET: INVERSE MATRICES
In problems 1- 2, verify that the given matrices are inverses of each other.
- [7321][1−3−27]
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- [1−1010−123−4][3−412−413−51]
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In problems 3- 6, find the inverse of each matrix by the row-reduction method.
SECTION 2.4 PROBLEM SET: INVERSE MATRICES
In problems 5 - 6, find the inverse of each matrix by the row-reduction method.
Problems 7 -10: Express the system as AX=B; then solve using matrix inverses found in problems 3 - 6.
- 3x−5y=2−x+2y=0
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- x+2z=8y+4z=8z=3
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SECTION 2.4 PROBLEM SET: INVERSE MATRICES
Problems 9 -10: Express the system as AX=B; then solve using matrix inverses found in problems 3 - 6.
- x+y−z=2x+z=72x+y+z=13
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- x+y+z=23x+y=7x+y+2z=3
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- Why is it necessary that a matrix be a square matrix for its inverse to exist? Explain by relating the matrix to a system of equations.
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- Suppose we are solving a system AX=B by the matrix inverse method, but discover A has no inverse. How else can we solve this system? What can be said about the solutions of this system?
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