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In Exercises 5-8, write B as a linear combination of the other matrices, if possible.
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Chapter 3 Solutions
Linear Algebra: A Modern Introduction
- Let X1,X2,X3 and b be the column matrices below. X1=[101], X2=[110], X3=[011] and b=[123] Find constants a, b, c and c such that aX1+bX2+cX3=barrow_forwardIn Exercises 23-28, let A=[102311201] and B=[230211164] Use the matrix-column representation of the product to write each column of AB as a linear combination of the columns of A.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. (A1X)1=A(B2A)1arrow_forward
- In Exercises 5-8, write B as a linear combination of the other matrices, if possible. 5.arrow_forwardLet A and B be square matrices of order 4 such that |A|=5 and |B|=3.Find a |A2|, b |B2|, c |A3|, and d |B4|arrow_forwardIn Exercises 23-28, let A=[102311201] and B=[230111164] Use the matrix-column representation of the product to write each column of BA as a linear combination of the columns of B.arrow_forward
- Use an example chosen from 22 matrices to show that for nn matrices A and B,ABBA but AB=BA.arrow_forwardIn Exercises 23-28, let and 24. Use the row-matrix representation of the product to write each row of AB as a linear combination of the rows of B.arrow_forwardIn Exercises 23-28, let and 27. Use the row-matrix representation of the product to write each row of BA as a linear combination of the rows of A.arrow_forward
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