In Exercises 1-6, list the minor matrix
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Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)
- In Exercises 47-52, assume that A and B are nn matrices with det A = 3 and det B=2. Find the indicated determinants. det (AAT)arrow_forwardIn 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_forwardIn 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[x1x2x3]=[x1+2x22x2x3],S[y1y2]=[y1y2y1+y2y1+y2]arrow_forward
- Prove 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_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_forwardLet A,D, and P be nn matrices satisfying AP=PD. Assume that P is nonsingular and solve this for A. Must it be true that A=D?arrow_forward
- Find the determinants in Exercises 35-40, assuming thatarrow_forwardIn Exercises 30-35, verify Theorem 3.32 by finding the matrix of (a) by direct substitution and (b) by matrix multiplication of [S] [T]. 32.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[x1x2]=[x1+2x23x1+x2],S[y1y2]=[y1+3y2y1y2]arrow_forward
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