2331_Test1_Practice_solFlagg

2331_Test1_Practice_solFlagg - Math 2331 Linear Algebra...

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Math 2331 Linear Algebra Test 1 - Chapters 1 and 2 Practice Problems Use the following vectors for questions 1-7 1 2 4 2 u ⎛⎞ ⎜⎟ = ⎝⎠ 1 0 1 0 v = 1 2 1 2 1 2 1 2 w = 1. Find u w i 2. Find u v i 3. Find 24 uw −+ 4. Find vw −− 5. Are v and w orthogonal?
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6. Find the length of each vector. 7. State a unit vector in the direction of u. Answer questions 8-12 for each of the following systems: 34 24 xy −= −− = 2 1 5 += 55 35 x y + = 8. Sketch the ROW PICTURE of the solution to the system. 9. Sketch the COLUMN PICTURE of the solution to the system. 10. State the system as a matrix equation. 11. State the elimination matrix E that transforms the system to upper triangular. 12. Solve by elimination and back substitution. 2
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1 5 xy −= +=
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55 35 x y xy += −+ =−
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State the LU and LDU factorization of each of the following matrices. 13. 13 45 A ⎛⎞ = ⎜⎟ ⎝⎠ 14. 123 230 304 B = 15. 2100 1210 0121 0012 C =
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Find the inverse, if it exists, of each of the following matrices.
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This note was uploaded on 02/21/2012 for the course MATH 2331 taught by Professor Staff during the Spring '08 term at University of Houston.

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2331_Test1_Practice_solFlagg - Math 2331 Linear Algebra...

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