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.
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