The matrix A is[img=44x19]1803b6ad8347a80.png[/img]. If the eqaution Ax=0 has only the trivial solution , thenA is invertible.
举一反三
- Let A be a [img=41x19]1803c4e38325ee9.png[/img] matrix, then ________. A: If Ax=0 has only trivial solution, then Ax=b must have a unique solution. B: If Ax=0 has a nontrivial solution, then Ax=b must have infinitely many solutions. C: If Ax=b has a unique solution, then Ax=0 must have a unique solution. D: If Ax=0 has a nontrivial solution, then [img=55x23]1803c4e38c0c9df.png[/img] must have a nontrivial solution.
- Ais an[img=44x19]1803b6a4c8dddc0.png[/img]matrix. A is not invertible if and only if 0 is an eigenvalue of A.
- Ais an[img=44x19]1803b6a4d11437c.png[/img]matrix. Number c is an eigenvalue of A if and only if (A-cI)x=0 has nontrial solutions.
- If I-AB is invertible, then I-BA is invertible. Where I is the identity matrix, and A is m by n, B is n by m.
- Let [img=99x19]1803c4e7d6c70bb.png[/img] be a linear transformation. If A is the standard matrix representation of [img=13x19]1803c4e7de70caa.png[/img], then an [img=44x19]1803c4e7e5f3add.png[/img] matrix B will also be a matrix representation of L if and only if B is similar to A.