Loading [MathJax]/jax/output/CommonHTML/jax.js

2024年2月23日 星期五

109年北科大電機碩士班-線性代數詳解

國立台北科技大學109學年度碩士班招生考試

系所組別: 2151電機工程系碩士班戊組
第一節 線性代數(選考)

解答:A=[03664537858939129615]R2R3R2[03664502442639129615]R2/2R2,R3/3R3[036645012213134325]3R2+R1R1,3R2+R3R3[000014012213102354]R1R3[102354012213000014]5R3+R1R1,R3+R2R2[1023024012207000014]rref(A)=[1023024012207000014]
解答:B=[Ab]=[354732416184]rref(B)=[1043101020000]{x143x3=1x2=2x=(43x312x3)={(43k12k)kR}

解答:[012100103010438001]4R2+R3R3[012100103010034041]3R1+R3R3[012100103010002341]R3+R1R1,3R3/2+R2R2[01024110092732002341]R1R2,R3/2R3[1009273201024100132212]A1=[9273224132212]

解答:B=[111112221233123n]R1+RkRk,k=2,,n[111101110122012n1]det(B)=|11112212n1|R1+RkRk,k=2,,n1|11101101n2||1112|=1det(B)=1

解答:A=[3531025710]=[13411][310001][47374747]A=[13411][(310)001][47374747]=[13411][0001][47374747]=[37374747]x=Ax0=[37374747][1212]=[3747]

解答:A=[b1b2b3]=[121011382]rref(A)=[100010001]rank(A)=3B is a basis of R3ab1+bb2+cb3=x[121011382][abc]=[354][abc]=A1x=[1043311321][354]=[205][x]B=[205]

解答:A=[123011114]C(A)={a(101)+b(211)+c(314)a,b,cR}rref(A)=[105011000][105011000][x1x2x3]=0{x1+5x3=0x2=x3ker(A)={k(511)kR}

解答:Let {u=(abc)v=(123)uvuv=0a2b3c=0u=a(101/3)+b(012/3){(101/3),(012/3)} is a basis which is orthogonal to va1=(101/3)e1=a1a1=310(101/3)a2=(012/3)e2=a2(a2e1)e1a2(a2e1)e1=57(1/513/5){(310,0,110),(135,535,335)} is a set of orthnonomal basiswhich is orthogonal to (1,-2,-3)

==================== END ======================
解題僅供參考,其他歷年試題及詳解

沒有留言:

張貼留言