线性代数第二版答案
篇一:工程数学线性代数课后同济第五版
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篇二:线性代数第二章答案
第二章矩阵及其运算
1?已知线性变换?
x1?2y1?2y2?y3?x2?3y1?y2?5y3?x3?3y1?2y2?3y3
求从变量x1?x2?x3到变量y1?y2?y3的线性变换?
解由已知?
x1221y1?
x2?315y2?x323y?23
y1221x1?7?49y1?故y2315x2?63?7y2?y323x32?4?3y32
y17x1?4x2?9x3
y2?6x1?3x2?7x3?y3?3x1?2x2?4x3
2?已知两个线性变换?1
y13z1?z2?x1?2y1?y3
x22y1?3y2?2y3y2?2z1?z3y3z2?3z3?x3?4y1?y2?5y3
求从z1?z2?z3到x1?x2?x3的线性变换?
解由已知
x1201y1201?31
x2232y223220?x415y4150?12?3
613z1?
12?49z210?116z3?0z1?1z2z?3?3?
x16z1?z2?3z3
因此有?x2?12z1?4z2?9z3?x310z1?z2?16z3
111123?
3?设A11?1B?1?24求3AB?2A及ATB1?11051?
111123111?
解3AB?2A?3?11?1?1?242?11?11?110511?11?
058111?21322?
3?0?562?11?12?1720?2901?11429?2?
111123058?
ATB11?1?1?24?0?56?1?11051290?
4?计算下列乘积?
4317?
(1)?1?232?5701?
43174?7?3?2?1?135?解?1?232?1?7?(?2)?2?3?1?6?57015?7?7?2?0?149?
3?
(2)(123)?2?1?
3?
解(123)?2(1?3?2?2?3?1)?(10)1?
2?
(3)?1?(?12)3?
2?(?1)2?2?242?
解?1?(?12)1?(?1)1?212?33?(?1)3?2?36?
1310?12?2140(4)?1?311?134?40?2?
1310?126?78?2140解?1?31?20?5?61?134?40?2?
a11a12a13x1?(5)(x1x2x3)a12a22a23?x2aaa?132333x3?
解
a11a12a13x1?(x1x2x3)a12a22a23?x2?aaa?132333x3?
x1?
(a11x1?a12x2?a13x3a12x1?a22x2?a23x3a13x1?a23x2?a33x3)?x2x3?
5?设A22?a11x12?a22x2?a33x3?2a12x1x2?2a13x1x3?2a23x2x31
12B1?13?0问?2
(1)AB?BA吗?
解AB?BA
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