Let A be a matrix with linearly independent columns. Select the best statement.

Q: Let A be a matrix with linearly independent columns. Select the best statement.

c) When A is a square matrix with all columns linearly independent then det(A) is non-zero. Then inverse of A exists and the solution is x=A^(-1) B for all B provided the product A^(-1) B is compatible.

ID: 1719962 • Letter: L

Question

Let A be a matrix with linearly independent columns. Select the best statement. You have only three attempts at this problem. The equation Ax = b has a solution for all b precisely when it has more rows than columns. There is no easy way to tell if Ax = b has a solution for all b The equation Ax = b has a solution for all b precisely when it is a square matrix. The equation Ax = b always has a solution for all b The equation Ax = b never has a solution for all b The equation Ax = b has a solution for all b precisely when it has more columns than rows, none of the above

Explanation / Answer

When A is a square matrix with all columns linearly independent then det(A) is non-zero.

Then inverse of A exists and the solution is x=A^(-1) B for all B provided the product A^(-1) B is compatible.

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Let A be a matrix with linearly independent columns. Select the best statement.

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