True or false (circle T or F). Let 0 denote the zero matrix of the appropriate size. T F If the matrix equation Ax = 0 with A an n x n matrix and 0 the nx1 zero vector has only the trivial solution x = 0 then A is row equivalent to the identity matrix. T F T F T F T F T F T F If the columns of n x n matrix A span R" then they are linearly independent. If the matrix equation Ax = b with A an n x n matrix and b an n x 1 vector has more than one solution then A is row equivalent to the identity matrix. If n x n matrix A is not invertible then AT is not invertible. If L is an n x n lower triangular matrix then so are L1 and L². If U is an n x n upper triangular matrix then so is UT. An n x n lower triangular matrix L is invertible if and only if all of its diagonal elements are nonzero.

True or false (circle T or F). Let 0 denote the zero matrix of the appropriate size. T F If the matrix equation Ax = 0 with A an n x n matrix and 0 the nx1 zero vector has only the trivial solution x = 0 then A is row equivalent to the identity matrix. T F T F T F T F T F T F If the columns of n x n matrix A span R" then they are linearly independent. If the matrix equation Ax = b with A an n x n matrix and b an n x 1 vector has more than one solution then A is row equivalent to the identity matrix. If n x n matrix A is not invertible then AT is not invertible. If L is an n x n lower triangular matrix then so are L1 and L². If U is an n x n upper triangular matrix then so is UT. An n x n lower triangular matrix L is invertible if and only if all of its diagonal elements are nonzero.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.3: Matrix Algebra

Problem 85E: Determine if the statement is true or false. If the statement is false, then correct it and make it...

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