sept3009 - Math 1502 D 1 School of Mathematics Math 1502...

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Unformatted text preview: Math 1502 D, September 30 2009 1 School of Mathematics Math 1502 Georgia Tech Calculus II, Section D Quiz # 5 September 30, 2009 First Name : Last Name : −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− 1. Let f, g be the two transformations below. For each of them indicate whether it is linear (YES) or not (NO). f( x )= y 3x − 5y −4x − 2y + 1 NO , g( x )= y x+y y 3 x2 NO . YES 2 2 YES 2 2 x 2. Let f ( )= y wer. x2 − y 2 . Is this map one-to-one ? Justify your ans2xy Math 1502 D, September 30 2009 2 0 −1 −1 −3 1 1 0 −4 2 and let x = −1 . Compute the third 3. Let A = 5 −6 3 0 −1 6 1 0 −1 1 entry of Ax without computing the whole vector Ax. Result = 4. Compute the inverse of the 2 × 2 matrix A = √ 5 −3 √ . 12 1 A−1 = Math 1502 D, September 30 2009 3 5. Let f be the linear transformation from R3 into R2 given first by a rotation of 45◦ around the x-axis (anti-clockwise in the plane yz ), followed by a rotation of 45◦ around the z -axis (anti-clockwise in the plane xy ) and by the projection parallel to the z -axis onto the plane z = 0. Compute the matrix Af of this transformation : Hint : compute the images of the vectors of the canonical basis Af = ...
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sept3009 - Math 1502 D 1 School of Mathematics Math 1502...

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