Ais an[img=44x19]1803b6a4c8dddc0.png[/img]matrix. A is not invertible if and only if 0 is an eigenvalue of A.
举一反三
- 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.
- The matrix A is[img=44x19]1803b6ad8347a80.png[/img]. If the eqaution Ax=0 has only the trivial solution , thenA is invertible.
- Which of the following statement is false? A: If[img=77x23]1803b6aa763b00a.png[/img], where[img=77x23]1803b6aa7e8aab9.png[/img] and D is a diagonal matrix, then B is a symmetric matrix. B: An orthogonal matrix is orthogonally diagonalizable. C: An[img=44x19]1803b6aa8680eb5.png[/img]symmetric matrix has n real eigenvalues. D: An[img=44x19]1803b6aa8680eb5.png[/img]symmetric matrix hasnlinearly independent eigenvectors.
- 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.
- The columns of the standard matrix for a linear transformation from [img=22x19]1803b6a8c19a71a.png[/img]to [img=25x19]1803b6a8c9f3863.png[/img] are the images of the columns of the [img=44x19]1803b6a8d3fc1b1.png[/img] indentity matrix.