solution6 - FIRST HOURLY PRACTICE VI Math 21b Fall 10 Name...

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10/7/2010 FIRST HOURLY PRACTICE VI 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 needed 1) T F A linear system with 2 equations and 3 unknowns has either infinitely many or no solutions.
2) T F If S is an invertible matrix which contains the vectors vectorv 1 , ...,vectorv n as columns, then vectorv 1 , . . . ,vectorv n is a basis of R n .
3) T F If A, B are given n × n matrices, then the formula ( A - B )( A + B ) = A 2 - B 2 holds.
4) T F Suppose A is an m × n matrix, where n < m . If the rank of A is m , then there is a vector y R m for which the system Ax = y has no solutions.
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6) T F The rank of an lower-triangular matrix equals the number of non-zero entries along the diagonal.
9) T F For any matrix A , one has dim(ker( A )) = dim(ker(rref( A ))).

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