110年 - 110 國立高雄科技大學_碩士班招生考試_電腦與通訊工程系：線性代號(甲組)#110418

科目：研究所、轉學考(插大)◆線性代號 | 年份：110年 | 選擇題數：0 | 申論題數：18

試卷資訊

所屬科目：研究所、轉學考(插大)◆線性代號

選擇題 (0)

申論題 (18)

(a) Compute AB.(5%)

(b) Compute 3A - B^T. (5%)

(a) Find the determinant of A. (5%)

(b) Find the inverse of A. (5%)

(c) Solve Ax = b for x₂. (5%)

(a) Find the rank of 4. (5%)

(b) Find a basis for the nuli space of A. (5%)

(c) Find the dimension of the null space of A. (5%)

(d) Determine whether or not the column vectors a₁, a₂, a₃ are linearly independent. Please answer independent or dependent. (5%)

(e) Find a nonzero vector x in R³, which is orthogonal to both a₁ and a₂. (5%)

(a) Find a matrix A such that L(x) = Ax for every x = in R³.(5%)

(b) Find the kernel of the linear transformation L (5%)

(c) Is Lone-to-one ? Please answer Yes or No. (5%)

(d) Is Lonto ? Please answer Yes or No. (5%)

5. [10%] Find the least squares solution of the linear system

(a) Find the eigenspace for A corresponding to the eigenvalue 2 = 1. (5%)

(b)Find all eigenvalues for A(other thanλ =1)除了λ =1以外的其他特徵值。(5%)

(c) Find a nonsingular matrix X and a diagonal matrix D such that A can be factored into a product A = . (10%)