(4)-5x+2y+2z+2t (5)(ah-bg(cf-ed) 1.用克拉默法则解定列线性方程组: 3x1+2x2+r3=5, x1+x2+2x3+3x4=0, x1+5x2+x3+2x4=0, 2x1+x2+3x3=11 x1+52+5x3+2x4=0; x1+2x2+33-2x4=6, 2x1+x2-5x3+x4=-14, 2x1+x2+2x3-3x4=8 3x1+2x2-x3+2x4=4 2x2+x3+2x4=9 2x1+3x2+2x3+x4=4; r1+4x2+7x3+6x4=20. 理:(1)|A4|=12,|B1=24,|B2 2,x3=3. (2)|4=-20.|B1=|B2=|B3=|B4=0.x1=x2=x3=x4=0 (3)|4=12,|B1=12,|B2|=24,|B3|=-12,|B4=-24,x1=1,x2=2,3=-1,x4=-2. (4)|4|=-9,B1=-9,|B2|=18,|B3=-27,|B4=-9,x1=1,x2=-2,x3=3,r4=1 2.求一个二次多项否f(x),使∫(1)=1,f(-1)=9,f(2)=3 4x+3 3.述明证次线性方程组 +… 0, +…+2xn=0, nr1+n2x2+…+nxn=0 仅有零解 交即:故结 1!12…m!≠0, 根据推论7.2,原方程只有零解 意对28 1.将定列行列否按拉普拉确定理展个,以求定列行列否们明 00 0.651(4) −5x + 2y + 2z + 2t. (5) (ah − bg)(cf − ed).
2–7 1. _`aDJ-t&@AB: (1)    3x1 + 2x2 + x3 = 5, 2x1 + 3x2 + x3 = 1, 2x1 + x2 + 3x3 = 11; (2)    x1 + 2x2 + 3x3 + 4x4 = 0, x1 + x2 + 2x3 + 3x4 = 0, x1 + 5x2 + x3 + 2x4 = 0, x1 + 5x2 + 5x3 + 2x4 = 0; (3)    x1 + 2x2 + 3x3 − 2x4 = 6, 2x1 + x2 + 2x3 − 3x4 = 8, 3x1 + 2x2 − x3 + 2x4 = 4, 2x1 + 3x2 + 2x3 + x4 = 4; (4)    2x1 + x2 − 5x3 + x4 = −14, x1 − 3x2 − 6x3 = −11, − 2x2 + x3 + 2x4 = 9, x1 + 4x2 + 7x3 + 6x4 = 20. : (1) |A| = 12, |B1| = 24, |B2| = −24, |B3| = 36, x1 = 2, x2 = −2, x3 = 3. (2) |A| = −20, |B1| = |B2| = |B3| = |B4| = 0, x1 = x2 = x3 = x4 = 0. (3) |A| = 12, |B1| = 12, |B2| = 24, |B3| = −12, |B4| = −24, x1 = 1, x2 = 2, x3 = −1, x4 = −2. (4) |A| = −9, |B1| = −9, |B2| = 18, |B3| = −27, |B4| = −9, x1 = 1, x2 = −2, x3 = 3, x4 = 1. 2. sHfbH :) f(x), ' f(1) = 1, f(−1) = 9, f(2) = 3. : f(x) = 2x 2 − 4x + 3. 3. STHt&@AB    x1 + x2 + · · · + xn = 0, 2x1 + 22x2 + · · · + 2nxn = 0, · · · · · · · · · · · · nx1 + n 2x2 + · · · + n nxn = 0 cGo-. : !" |A| = ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ 1 1 · · · 1 2 22 · · · 2 n . . . . . . . . . . . . n n2 · · · n n ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ = 1!2! · · · n! 6= 0, =>^# 7.2, K@A{Go-.
2–8 1. v )[`c`def, $s ): (1) ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ 5 6 0 0 0 1 5 6 0 0 0 1 5 6 0 0 0 1 5 6 0 0 0 1 5 ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ; (2) ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ a 0 b 0 0 c 0 d y 0 x 0 0 w 0 z ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ; · 7 ·