Solved: Construct 3 × 2 matrices A and B such that Ax = 0

Chapter 1, Problem 29E

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QUESTION:

PROBLEM 29EConstruct 3 × 2 matrices A and B such that Ax = 0 has a nontrivial solution, but Bx = 0 has only the trivial solution.

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QUESTION:

PROBLEM 29EConstruct 3 × 2 matrices A and B such that Ax = 0 has a nontrivial solution, but Bx = 0 has only the trivial solution.

ANSWER:

Solution :

  Step 1 :   Construct 3 × 2 matrices A and B such that Ax = 0 has a nontrivial solution,

               but Bx = 0 has only the trivial solution.

               A:  matrix with non zero column such that neither column is a multiple of other.

               B: any matrix with one column a multiple of another.

 

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