Ans-Lin-Alg - Part I Linear Algebra Exercises 1.1 1 3 6 8 12 15 x = 4 y = 1 The set of points on the line x 2y = 4 x = 2 y = 1 x = 2 y = 3 x = 3 2y

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Part I. Linear Algebra Exercises 1.1 1. x =4 ,y =1 3. The set of points on the line x +2 y 6. x =2 = - 1 8. x = - 2 =3 12. x = - 3+2 y, z =0 any real number 15. x ,z Exercises 1.2 3. Coefficient matrix: rank 2; augmented matrix: rank 2; x - 2 a, y = a, z = - 2 ,a any real number 4. Coefficient matrix: rank 2; augmented matrix: rank 3; no solution 7. Coefficient matrix: rank 3; augmented matrix: rank 3; x 1 =8+2 a - 3 b, x 2 = a, x 3 = - 1 - 2 b, x 4 = b, x 5 = - 3 ,b any real numbers 13. x 1 =10 / 7 ,x 2 / 7 3 / 2 19. x 1 - 2 a, x 2 = a, x 3 4 any real number 21. no solution 23. ( i ) k ± = - 3 , 2( ii ) k = - 3( iii ) k 25. (a) no (b) no (c) yes 26. 124 - 13 0 132 22 - 2 234 341 100 11 / 31 8 / 3 010 1 / 30 - 4 / 3 001 - 4 / 35 1 / 6 Exercises 1.3 3. yes 1
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4. yes 5. No; the leading 1 in the 3,5-position is not the only nonzero entry in its column. 6. 8. yes 11. x = - 3 - a, y =2+2 a, z = a, a any real number 13. x 1 =11 - 2 a + b, x 2 = a, x 3 =3 - b, x 4 = b, a, b any real numbers 18. x = y = z = 0, the trivial solution 21. x 1 =2 a - b, x 2 = - a +4 b, x 3 = a, x 4 = b, a, b any real numbers 28. a = bb any real number 29. a =4 Exercises 1.4 3. (a) - 4 - 3 28 - 6 - 20 24 (e)
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This note was uploaded on 01/06/2011 for the course MATH 3333 taught by Professor Staff during the Spring '08 term at University of Houston.

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Ans-Lin-Alg - Part I Linear Algebra Exercises 1.1 1 3 6 8 12 15 x = 4 y = 1 The set of points on the line x 2y = 4 x = 2 y = 1 x = 2 y = 3 x = 3 2y

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