Solved: PROBLEM 44E[M] Repeat Exercise 43 with the Problem 44E Chapter 1.7

Linear Algebra and Its Applications | 5th Edition

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Problem 44E

[M] Repeat Exercise 43 with the matrices A and B from Exercise 42. Then give an explanation for what you discover, assuming that B was constructed as specified.Exercise 43:[M] With A and B as in Exercise 41, select a column v of A that was not used in the construction of B and determine if v is in the set spanned by the columns of B. (Describe your calculations.)Exercise 41:[M] Use as many columns of A as possible to construct a matrix B with the property that the equation Bx = 0 has only the trivial solution. Solve Bx = 0 to verify your work. Exercise 42:[M] Use as many columns of A as possible to construct a matrix B with the property that the equation Bx = 0 has only the trivial solution. Solve Bx = 0 to verify your work.

Step-by-Step Solution:

Solution :Step 1 :The objective is to show that each linearly dependent column in A is in the set spanned by the column of B.Step 2 : In exercise 42 , i calculate the rank of the matrix will be 4 by RREF method.And in the exercise 43 , i calculate the rank of the matrix will 3 by RREF method

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ISBN: 9780321982384

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