# Problem 1 TF questions 20 points No justifications are...

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10/7/2010 FIRST HOURLY PRACTICE III Math 21b, Fall 10 Name: MWF10 Oliver knill MWF11 Anand Patel Start by writing your name in the above box and check your section in the box to the left. Try to answer each question on the same page as the question is asked. If needed, use the back or the next empty page for work. If you need additional paper, write your name on it. Do not detach pages from this exam packet or un- staple the packet. Please write neatly and except for problems 1-3, give details. Answers which are illegible for the grader can not be given credit. No notes, books, calculators, computers, or other electronic aids can be allowed. You have 90 minutes time to complete your work. 1 20 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 Total: 110 1
Problem 1) TF questions (20 points) No justifications are needed. 1) T F A rotation in the plane around the point (1 , 1) by angle 90 0 is a linear transformation.
2) T F If ABC = I 2 for 2 × 2 matrices A, B, C , then A is invertible.
3) T F There is a 2 × 3 matrix A and a 3 × 2 matrix B such that AB = BA .
4) T F For any linear system Ax = b with 3 × 3 matrix A , the augmented 3 × 4 matrix B = [ A | b ] satisfies rank(A) = rank(B).
5) T F If the system Ax = b has a unique solution for some b , then A must be a square matrix. 6) T F If v 1 , . . . , v 4 are linearly independent vectors in R
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8) T F For any two 3 × 3 matrices A, B the identity ( A + B )( A + B ) = A 2 +2 AB + B 2 holds.
9) T F The set X of quadratic polynomials satisfying f (0) = f (0) is a linear space.
10) T F If A is a non-invertible matrix then rref( A ) has at least one row of zero.
11) T F The plane 2 x + 3 y + 5 z 10 = 0 is the image of a linear transformation T .
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12) T F
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