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It A is an invertible nxn matrix, then the inverse of matrixA IS A A3D det A adj A and ad - bc+ 0, then Ais invertible and the inverse is c d 1 d -b Show that if A is 2x2, then the first theorem gives the same formula for A-1 as that given by the second theorem. ad - bc - C a What must be done to prove the theorems are equivalent? O A. Evaluate the determinant of matrix A = d -b using A 1 adj A det A a O B. Evaluate the inverse of matrix A = a b using A %3D c d det A adj A OC. Evaluate the determinant of matrix A = | a b 1 d -b using A %3D c d ad - bc a O D. Evaluate the inverse of matrix A= d -b using A 1 adj A. det A

It A is an invertible nxn matrix, then the inverse of matrixA IS A A3D det A adj A and ad - bc+ 0, then Ais invertible and the inverse is c d 1 d -b Show that if A is 2x2, then the first theorem gives the same formula for A-1 as that given by the second theorem. ad - bc - C a What must be done to prove the theorems are equivalent? O A. Evaluate the determinant of matrix A = d -b using A 1 adj A det A a O B. Evaluate the inverse of matrix A = a b using A %3D c d det A adj A OC. Evaluate the determinant of matrix A = | a b 1 d -b using A %3D c d ad - bc a O D. Evaluate the inverse of matrix A= d -b using A 1 adj A. det A

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section: Chapter Questions
Problem 1RQ
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If A is an invertiblenxn matrix, then the inverse of matrix A is A1=- det A a b and ad - bc 0, then Ais invertible and the inverse is c d adj A. If A = d -b Show that if A is 2x2, then the first theorem gives the same formula for A1 as that given by the second theorem. ad - bc - c a What must be done to prove the theorems are equivalent? O A. Evaluate the determinant of matrix A = d -b using A 1 %3D det A adj A a B. Evaluate the inverse of matrix A= using A c d a b 1 %3D det A adj A a b O C. Evaluate the determinant of matrix A = 1 1 d - b using A c d ad - bc a d -b using A 1 O D. Evaluate the inverse of matrix A = -adj A. - C a det A
Transcribed Image Text:If A is an invertiblenxn matrix, then the inverse of matrix A is A1=- det A a b and ad - bc 0, then Ais invertible and the inverse is c d adj A. If A = d -b Show that if A is 2x2, then the first theorem gives the same formula for A1 as that given by the second theorem. ad - bc - c a What must be done to prove the theorems are equivalent? O A. Evaluate the determinant of matrix A = d -b using A 1 %3D det A adj A a B. Evaluate the inverse of matrix A= using A c d a b 1 %3D det A adj A a b O C. Evaluate the determinant of matrix A = 1 1 d - b using A c d ad - bc a d -b using A 1 O D. Evaluate the inverse of matrix A = -adj A. - C a det A
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