1920t1math1030cw3sol.pdf - 2019 MATH1030 Classwork 3 Last updated • online exercise The following webpage will be set up on Thursday Sep 26 Link

# 1920t1math1030cw3sol.pdf - 2019 MATH1030 Classwork 3 Last...

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(a) 2 1 2 3 0 4 2 - 3 1 1 2 0 1 x = - 1 1 0 0 5 - 2 (b) x 1 3 4 2 1 - 1 + 4 3 6 0 1 1 = 7 12 6 6 4 2 Answer. (a) The left hand side of the equation is equal to - 1 1 0 0 5 4 - 3 x . Hence x must satisfy the equation 4 - 3 x = - 2, implying that x = 2. (b) The left hand side of the equation is equal to x + 4 3 x + 3 4 x + 6 2 x x + 1 - x + 1 . Equating the (1 , 1) entries of both sides gives the equation x + 4 = 7, so that x = 3. Equating the (2 , 3) entries of both sides gives the equation - x + 1 = 2, which is not satisfied by x = 3. Hence, the original equation has no solution. 3. Compute the following. (a) 1 2 - 1 1 1 1 1 1 - 1 - 1 0 0 2 3 (b) 1 1 3 5 - 1 1 0 - 2 1 1 1 - 1 1 1 0 1 1 2 0 0 (c) 2 1 2 3 4 0 1 0 1 - 1 - 1 1 0 - 3 0 1 1 2 1 1 1 1 0 - 1 - 1 - 1 1 1 2 1 - 1 0 0 - 1 Answer. (a) 1 1 3 5 - 1 - 1 3 4 1 1 1 2 2
(b) 4 8 - 1 0 2 4 (c) 1 1 - 2 - 3 - 5 - 4 4. (a) Let A = 1 0 1 0 1 1 0 0 2 , B = 1 1 2 1 0 0 0 1 1 . Find AB and BA . (b) Let a, b, c, d be real numbers and let A = 1 0 a b 0 1 c d , B = - a - b - c - d 1 0 0 1 . Find AB and BA . Answer. (a) AB = 1 2 3 1 1 1 0 2 2 BA = 1 1 6 1 0 1 0 1 3 (b) AB = 0 0 0 0 BA = - a - b - a 2 - bc - ab - bd - c - d - ac - cd - bc - d 2 1 0 a b 0 1 c d 5. (a) Let A = 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 . Find A 2 . (b) Let B = 1 0 1 5 1 3 1 - 1 2 , C = - 5 1 1 7 - 1 - 2 6 - 1 - 1 .

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