Math 636 Midterm Quiz x1 2 1. The geometric interpretation of the following set W = R | x1 + x2 = 2 is x2 (a) a point in R2 . (b) a line in R2...
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can I also please have help on #25- 30 please please? Linear Algebra

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Math 636 Midterm Quiz 1. The geometric interpretation of the following set W = ±² x 1 x 2 ³ R 2 | x 1 + x 2 = 2 ´ is (a) a point in R 2 . (b) a line in R 2 passing through the origin. (c) a line in R 2 not passing through the origin. (d) all of R 2 . 2. The geometric interpretation of the set S of all vectors ~x R 4 that are orthogonal to 1 0 1 - 1 , 0 2 1 1 , and 1 1 1 - 2 is (a) a point in R 4 . (b) a line in R 4 . (c) a plane in R 4 . (d) a hyperplane in R 4 . 3. Let ~v 1 ,~v 2 ,~v 3 ,~v 4 be non-zero vectors in R 4 such that the solution set of the system µ ~v 1 ~v 2 ~v 3 ~v 4 ~ 0 is a hyperplane. What is the geometric interpretation of Span { ~v 1 ,~v 2 ,~v 3 ,~v 4 } ? (a) A point in R 4 . (b) A line in R 4 . (c) A plane in R 4 . (d) A hyperplane in R 4 . 4. Which of the following is a scalar equation for the plane in R 3 with vector equation ~x = s 1 - 1 0 + t 1 2 3 + 1 1 1 , s,t R (a) - x 1 - x 2 + x 3 = - 1 (b) x 1 + x 2 + x 3 = 1 (c) 3 x 1 + 3 x 2 + 3 x 3 = - 1 (d) x 1 - x 2 = 6 1
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2 5. Which of the following is a vector equation for the plane in R 3 with scalar equation x 1 - x 2 + 2 x 3 = 0. (a) ~x = s 1 0 2 + t 0 - 1 2 , s,t R . (b) ~x = - 1 1 1 + s 2 0 - 1 + t 2 2 0 , s,t R (c) ~x = s 1 - 1 2 + t 2 - 2 4 , s,t R . (d) ~x = 1 1 - 1 + s 1 1 0 + t - 2 0 1 , s,t R 6. Let A = 1 8 7 - 7 1 - 1 1 1 1 - 1 3 1 - 3 - 3 4 1 . Then (a) det A = - 24. (b) det A = 84. (c) det A = 24. (d) det A = - 84. 7. If T = x 1 x 2 x 3 R 3 | x 1 + 2 x 2 = 3 x 3 , then (a) dim T = 1. (b) dim T = 2. (c) dim T = 3. (d) T is not a subspace of R 3 . 8. If U = Span { 3 + x + 3 x 2 , 1 + 2 x + x 2 , 1 - 3 x + x 2 ,x } is a subspace of P 2 ( R ), then (a) dim U = 1. (b) dim U = 2. (c) dim U = 3. (d) dim U = 4.
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