In Exercises30-35, verify Theorem 3.32 by finding the matrix of
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Chapter 3 Solutions
Linear Algebra: A Modern Introduction
- In Exercises30-35, verify Theorem 3.32 by finding the matrix of ST (a) by direct substitution and (b) by matrix multiplication of [S] [T]. T[x1x2]=[x1x2x1+x2],S[y1y2]arrow_forwardLet A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and nullity of AB. b Show that matrices A and B must be identical.arrow_forwardIn Exercises 30-35, verify Theorem 3.32 by finding the matrix of ST (a) by direct substitution and (b) by matrix multiplication of [S] [T]. T[x1x2x3]=[x1+x2x32x1x2+x3],S[y1y2]=[4y12y2y1+y2]arrow_forward
- In Exercises 30-35, verify Theorem 3.32 by finding the matrix of ST (a) by direct substitution and (b) by matrix multiplication of [S] [T]. T[x1x2]=[x1+2x23x1+x2],S[y1y2]=[y1+3y2y1y2]arrow_forwardTrue or false? det(A) is defined only for a square matrix A.arrow_forwardProve part b of Theorem 1.35. Theorem 1.35 Special Properties of Let be an arbitrary matrix over. With as defined in the preceding paragraph,arrow_forward
- Let A and B be square matrices of order n over Prove or disprove that the product AB is a diagonal matrix of order n over if B is a diagonal matrix.arrow_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. XA2=A1arrow_forward
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