103年 - 103 淡江大學 轉學考 線性代數#55733

科目：轉學考-線性代數 | 年份：103年 | 選擇題數：0 | 申論題數：10

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申論題 (10)

【已刪除】1. (10 pts) Determine if the set S = {(1,2,3), (0，1,1), (2,5,1)} forms a basis for .
(a) Find the eigenvalues of A.
(b) Find an invertible matrix P such that P-lAP is diagonal.
(c) Use the result in (b) to compute A10.
(a) Find an orthonormal basis for IV.
(b) What is the dimension of W⊥ (orthogonal complement of M,)? Justify your answer.
【已刪除】 (a) Find the matrix representation of T relative to the standard basis for M2,2
(b) Determine if T is invertible.
【已刪除】5. (10 pts) Let T : be a linear transformation. If  is a linearly dependent set in En, show that the set,  is also linearly dependent.
【已刪除】6. (10 pts) Suppose matrices A and B have the same characteristic polynomial
Is it true that A and B must be similar? Why?