109年 - 109 東吳大學_轉學生招生考試_數學系三年級︰線性代數#105826

1. (20%) Consider the homogeneous linear system 3x- y + 2z +w =0 62- - 2y - 4z =0. Find a basis for the solution space, and find the dimension of that space.

2. (20%) Let, and Hn, be the set of all n x n symmetric matrices. Prove that H_n is a subspace of the space of n x n matrices. Find a basis for H₄. What is dim(H₄)?

3. (20%) Let A =.Find the inverse of A.

4. (20%) Apply Gram-Schmidt Orthonormalization process to the vectors น1 = (1, 1,1),u2 = (1,0, -1),u3 = (2,1, -1) with respect to the stan- dard inner product.

5. (20%) . Find an orthogonal matrix Q so that Q^TAQ is a diagonal matrix.

109年 - 109 東吳大學_轉學生招生考試_數學系三年級︰線性代數#105826

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