87年 - 87 淡江大學轉學考線性代數#56385

科目：轉學考-線性代數 | 年份：87年 | 選擇題數：0 | 申論題數：12

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所屬科目：轉學考-線性代數

選擇題 (0)

申論題 (12)

【已刪除】1. Find the kernel of the linear transformation T : R³ → R³ defined by

(10%)

【已刪除】2(a)-Eind the rank of the matrix

(10%)

(b) Determine whether the matrix given in (a) is invertible., (5%)

(a) Find the matrix representation A of T relative to B = {l，x，x²，x³}. ,(5%)

(b) Find the change-coordinates matrix from B to B' = {x,1 + x,x+ x²,x³}. (5%)

(c) Find the matrix representation Ar of T relative to B'. (5%)

【已刪除】

5. Let A and B be both nx n matrices. Prove that the product AB is invertible if and only if both A and B are invertible. (10%).

,(a) Find the characteristic polynomial of A. (5%)

(b) Find the real eigenvalues and the corresponding eigenspaces of A. (10%)

(c) Determine whether the matrix A given in (a) is diagonalizable; if yes, please diagonalize it. (5%)

【已刪除】7.

. Find a Jorden basis and the corresponding Jorden canonical form for A. (20%)