Question. Consider the matrix M = 0 6 -6 t+1 12 t-2 0 t +7 2 where t is a real number. (a) Evaluate the determinant of M in terms of t.. (b) For what value(s) of t does M have an inverse? Explain your answer. (c) The rank of M depends on t. Determine the different possibilities for the rank, and give the corresponding value(s) of t.

Question. Consider the matrix M = 0 6 -6 t+1 12 t-2 0 t +7 2 where t is a real number. (a) Evaluate the determinant of M in terms of t.. (b) For what value(s) of t does M have an inverse? Explain your answer. (c) The rank of M depends on t. Determine the different possibilities for the rank, and give the corresponding value(s) of t.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.2: Determinants

Problem 33EQ

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Similar questions

True or False ? a The determinant of a 22 matrix A is a21a12a11a22. b The determinant of a matrix of order 1 is the entry of the matrix. c The ij-cofactor of a square matrix A is the matrix obtained by deleting the ith row and jth column of A
True or False ? a To find the determinant of a triangular matrix, add the entries on the main diagonal. b To find the determinant of a matrix, expand by cofactors in any row or column. c When expanding by cofactors, you need not evaluate the cofactors of zero entries.

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