hw10s - -1 1 1*1-3-1 1 2*2-6-1 1 3*3-3 = 0(d By cofactor...

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MATH 4377, ADVANCED LINEAR ALGEBRA, SUMMER 2011, Key to HW#10 Due date: Thursday, June 30th 1. Probelm 2 (a) on Page 208. Solution . The determinant is 30 2. Probelm 6, 7, 12 on P. 221. Solution . 6: det(A) = ( - 1) 1+1 *1*(-15) + ( - 1) 1+2 *0*5 + ( - 1) 1+3 *2*1 = -13 7: det(A) = ( - 1) 2+1 *(-1)*(-6) + ( - 1) 2+2 *0*(-4) + ( - 1) 2+3 *(-3)*(-2) = -12 12: det(A) = ( - 1) 4+1 *(-2)*(-52) + ( - 1) 4+2 *6*42 + ( - 1) 4+3 *(-4)*(-2) + ( - 1) 4+4 *1*14 = 154 3. Probelm 4, 7 on Page 228 Solution . 4: A = 2 1 - 3 1 - 2 1 3 4 - 2 X 1 = det(M 1 )/det(A) = -1, X 2 = det(M 2 )/det(A) = 4/5, X 3 = det(M 3 )/det(A) = 3/5. 7: A = 3 1 1 - 2 - 1 0 1 2 1 x 1 = det(M 1 )/det(A) = 0, x 2 = det(M 2 )/det(A) = -12, x 3 = det(M 3 )/det(A) = 16. 1

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4. Problem 4(a), (d), (h), on P. 237. Solution . 4(a): By cofactor expansion along the ﬁrst row, det(A) = (
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Unformatted text preview: -1) 1+1 *1*(-3) + (-1) 1+2 *2*(-6) + (-1) 1+3 *3*(-3) = 0. (d) By cofactor expansion along the ﬁrst row, det(A) = (-1) 1+1 *1*(-1) + (-1) 1+2 *(-2)*13 + (-1) 1+3 *3*(-5) = 10 (h) 1-2 3-12-5 12-14 19-9 22-20 31-4 9-14 15 -→ 1-2 3-12 2 1-41 4 7-77 1-2-33 -→ 1-2 3-12 1-2-33 5 25 15 55 -→ 1-2 3-12 1-2-33 5 25-20 So det(A) = -100 2...
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hw10s - -1 1 1*1-3-1 1 2*2-6-1 1 3*3-3 = 0(d By cofactor...

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