109年 - 109東吳大學_碩士班招生考試_數學系：線性代數#100494

2.  . Find an invertible matrix S that diagonalizes A, and compute AS. Apply the result, compute , where is defined by 

4.  Let T : be defined by T(A) = . Prove
that T is a linear map, and find the matrix representation of T with
respect to the basis

where is the transpose of A.

5. State the Cauchy-Schwarz inequality in . Applying the inequal- ity to show 9 ≤ (a+b+c) for all positive real numbers a, b, c, and also x + 2y + 3z ≤ √14 on the sphere x² + y² + z² = 1.