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Solved: PROBLEM 44E[M] Repeat Exercise 43 with the
Chapter 1, Problem 44E(choose chapter or problem)
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.
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QUESTION:
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.
ANSWER: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.