# hw2answers - rows of this matrix 3.d Not possible beacuse...

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MATH 343:001 Applied Linear Algebra Fall 2010 Answers to Homework 2 questions 1.a. M 1 = ± 0 3 1 - 2 ² 1.b. M 2 = ± 1 1 2 3 ² - 1 = ± 3 - 1 - 2 1 ² 1.c. M 2 M 1 = ± - 1 11 1 - 8 ² 2.a. A = ± 0 1 - 1 1 2 1 ² 2.b. B = ± - 8 / 5 - 13 / 5 - 7 / 5 4 / 5 9 / 5 1 / 5 ² 2.c. L ( v ) C = B h 5 - 3 1 i = h - 8 / 5 - 6 / 5 i 3.a. 1 2 3 2 0 0 3 0 0 3.b. This is not possible because the null space is orthogonal to the row space, and a non-zero vector cannot be orthogonal to itself. 3.c. 1 1 1 0 0 1 . Notice that the vectors ³ 1 2 ´ and ³ 2 1 ´ can be obtained as linear combinations of the
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Unformatted text preview: rows of this matrix. 3.d. Not possible beacuse the dimensions of the column and row spaces must agree. 4. ± 7 / 5 4 / 5 ² 6. The normal equations are Mx = b where M = ± 23635064 11908 11908 6 ² b = ± 4150900 . 22 2090 . 29 ² The equation of the line is y = 1 . 43427419 x-2498 . 17452. Gerardo Laﬀerriere, October 20, 2010...
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