quiz1_F06, no solutions

quiz1_F06, no solutions - Let a 1 = 1 1 2 a 2 =-1 3 b = 2...

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MATH 202, QUIZ #1 Due Friday, October 6, before 3 PM strict Covers Chapters 1–2 of textbook Time: one hour Your name (print): . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Your instructor : . . . . . . . . . . . . . . . . . . . Time your class meets : . . . . . . Please show all work. Books, notes and calculators are not permitted on this quiz. Write below and sign the Pledge: I pledge my honor that I have not violated the Honor Code during this examination.
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1. (20 points) Find all vectors b 1 b 2 b 3 such that the system x + 2 y + z = b 1 x - y + 4 z = b 2 2 x + y + 5 z = b 3 is consistent.
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Unformatted text preview: Let a 1 = 1 1 2 , a 2 = -1 3 , b = 2 2-3 . Is b a linear combination of a 1 , a 2 ? Explain why or why not. 3. (20 points) Find the inverse of the matrix A = 1 1 2 1 2-1 3 . 4. (20 points) Let L : R 2 → R 2 be a linear transformation such that L ± 3 1 ² = ± 2-1 ² and L ± 2 1 ² = ± 2 ² . Find a 2 × 2 matrix A such that L ( x ) = Ax for all x in R 2 . 5. (20 points) Find all 2 × 2 matrices X , which satisfy AX = XA for A = ± 1 2 3 ² ....
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