Solved: True or False? In Exercises 71 and 72, determine whether each statement is true
Chapter 3, Problem 71(choose chapter or problem)
In Exercises 71 and 72, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows that the statement is not true in all cases or cite an appropriate statement from the text.
(a) If A is an \(n \times n\) matrix and c is a nonzero scalar, then the determinant of the matrix cA is \(n c \cdot \operatorname{det}(A)\).
(b) If A is an invertible matrix, then the determinant of \(A^{-1}\) is equal to the reciprocal of the determinant of A.
(c) If A is an invertible \(n \times n\) matrix, then Ax = b has a unique solution for every b.
Text Transcription:
n times n
nc cdot det(A)
A^-1
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