104年 - 104 淡江大學轉學考線性代數#53164

科目：轉學考-線性代數 | 年份：104年 | 選擇題數：0 | 申論題數：7

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申論題 (7)

【已刪除】1. (20 %) Find the characteristic polynomial and the eigenvalues for the 3x3 matrix A

【已刪除】2. (10 %) Find the inverse matrix B^-1 for the 3x3 matrix B=

(1) Find an invertible 3x3 matrix P and a 3 x 3 diagonal matrix D such that P^-1AP = D.

(2) Calculate A⁵.

【已刪除】4. (20 points) Let

【已刪除】5. (20 points) Let V be the vector space of 2 x 2 matrices, and let T : V V be defined by

Find the matrix of T with respect to the basis C = {A₁,A₂, A₃, A₄}, where

6. (10 points) Let T : V → V" be a one-to-one linear transformation and dim(V) = n. Show that T is onto.