The Inverse of a Matrix: In Exercises 5-12, show that
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- The Inverse of a Matrix In Exercises 1-6, show that B is the inverse of A. A=-2231-10014, B=13-4-53-4-83120arrow_forwardIn Exercises 20-23, solve the given matrix equation for X. Simplify your answers as much as possible. (In the words of Albert Einstein, Everything should be made as simple as possible, but not simpler.) Assume that all matrices are invertible. ABXA1B1=I+Aarrow_forwardWhich of the following operations can we perform for a matrix A of any dimension? (i) A+A (ii) 2A (iii) AAarrow_forward
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- Use elementary matrices to find the inverse of A=100010abc, c0.arrow_forwardTrue or False ? In Exercises 71 and 72, determine whether each statement is true or false. If a statement is true or false. If a statement is true, give a reason or cite an appropriaste statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. a The inverse of the inverse of a non-singular matrix A, A-1-1, is equal to A itself. b The matrix abcd is invertible when ab-dc0. c If A is a square matrix, then the system of linear equations Ax=b has a unique solution.arrow_forwardFinding the Inverse of a 22 Matrix In Exercises 31-36, use the formula on page 66 to find the inverse of the 22 matrix if it exists. 72-341545arrow_forward
- Similar Matrices In Exercises 19-22, use the matrix P to show that the matrices A and Aare similar. P=A=A=[11201]arrow_forwardSimilar Matrices In Exercises 19-22, use the matrix Pto show that the matrices Aand Aare similar. P=[111011001], A=[500030001], A=[522032001]arrow_forwardTrue or False? In Exercises 41 and 42, 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 the statement is not true in all cases or cite an appropriate statement from the text. a The identity matrix is an elementary matrix. b If E is an elementary matrix, then 2E is an elementary matrix. c The inverse of an elementary matrix is an elementary matrix.arrow_forward
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