110年 - 110 國立臺灣大學_碩士班招生考試_工程科學及海洋工程學研究所丁組:線性代數(B)#100700

科目：研究所、轉學考(插大)◆線性代數 | 年份：110年 | 選擇題數：0 | 申論題數：11

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所屬科目：研究所、轉學考(插大)◆線性代數

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申論題 (11)

(a) If A and B are symmetric then AB is symmetric.

(b) If AB = Bthen A = I.

(c) All geometric progressions

(d) If subspace V is orthogonal to W, then

(e) If A is invertible and B is singular, then A + B is invertible.

(a) Find an orthonormal basis for the column space of A.

(b) Write A as QR, where Q has orthonormal columns and R is upper triangular.

(c) Find the least-squares solution to Ax = b, if b = [ -3, 7, 1, 0, 4]^T.

4.

5.Find the 3 by 3 symmetric matrix A and its pivots, rank, eigenvalues, and determinant: (20%)

6.Identify the curve and sketch the graph. x² + xy+ y²+ 3x + 3y = 3.(10%)