quiz1_F07_solns

quiz1_F07_solns - MATH 202 QUIZ 1 Wednesday Covers Chapter...

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Unformatted text preview: MATH 202 - QUIZ # 1 Wednesday, October 10, 2007 Covers Chapter 1 and Chapter 2 of the text 1. (12 points) Find all solutions to the linear system 2 x + y + z = 7 x + 3 y − 2 z = 1 8 x + 9 y − z = 23 Interpret the result geometrically. The augmented matrix for this system reduces to 1 0 1 4 0 1 − 1 − 1 0 0 So we conclude that x = 4 − z , y = − 1 + z and z varies freely. The three given equations each define a plane and these three planes intersect in the line through (4 , − 1 , 0) and parallel to ( − 1 , 1 , 1). 2. (12 points) Let T : R 2 → R 3 be a linear transformation such that T parenleftBigg 2 1 parenrightBigg = 1 3 6 and T parenleftBigg 5 3 parenrightBigg = 10 15 21 Find the matrix of T . The matrix A for this transformation satisfies the equation A parenleftBigg 2 5 1 3 parenrightBigg = 1 10 3 15 6 21 To solve we invert and multiply: parenleftBigg 2 5 1 3 parenrightBigg- 1 = 1 6 −...
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quiz1_F07_solns - MATH 202 QUIZ 1 Wednesday Covers Chapter...

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