Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

For each of the following statements, indicate whether the statement is true or

ID: 3823159 • Letter: F

Question

For each of the following statements, indicate whether the statement is true or false. If a matrix A is singular, then the number of solutions to the linear system Ax = b depends on the particular choice of right-hand-side b. If a matrix A is nonsingular, then the number of solutions to the linear system Ax = b depends on the particular choice of right-hand-side b. If a matrix has a very small determinant, then the matrix is nearly singular. If any matrix has a zero on its main diagonal, then it is necessarily singular.

Explanation / Answer

Statement number 1 is T

If a matrix A is singular then the number of solutions depends on b.

Statement number 2 is F.

If A is non singular then Ax = b has unique solution.

Statement number 3 is T.

It is not easy to compute inverse of a matrix . Small determinant may also be due to matrix entries of low magnitude.

Statement number 4 is F.

2 by 2 matrix counter example.