Show that the block upper triangular matrix A in Example 5 is invertible if and only if both A11 and A22 are invertible. [Hint: If A11 and A22 are invertible, the formula for A−l given in Example 5 actually works as the inverse of A.] This fact about A is an important part of several computer algorithms that estimate eigenvalues of matrices. Eigenvalues are discussed in Chapter 5.
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Chapter 2 Solutions
Linear Algebra And Its Applications
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