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MAT211_PracticeMidterm1Sol[1]

MAT211_PracticeMidterm1Sol[1] - 1 IMPORTANT NOTE These...

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Unformatted text preview: 1 IMPORTANT NOTE: These IMPORTANT NOTE: These are the answers. In the are the answers. In the exam you need to add justifcations exam you need to add justifcations Example (3.3-27) Determine whether the following vectors form a basis of R 4 (1,1,1,1), (1,-1,1,-1),(1,2,4,8),(1,-2,4,-8) Answer: Yes, (the matrix with these vectors as columns is invertible) Exercise 1.2-30 Find the polynomial of degree 3 whose graph passes through the points (0,1),(1,0),(-1,0), (2,-15) Find the inverse of the rotation matrix. cos(a)-sin(a) sin(a) cos(a) cos(a) sin(a)-sin(a) cos(a) Answer= Let T be a clockwise rotation in R 2 by π /2 followed by an orthogonal projection onto the y axis. 1. Find the matrix of T. 2. Determine whether T is invertible 3. Find im(T) and ker(T) Answer: It was given in class. Find the inverse of the matrix and check your answer. Interpret your result geometrically. a b b-a a b b-a Answer: The matrix is a re¡ection about a line L followed by a scaling by (a 2 + b 2 ) 1/2 ....
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MAT211_PracticeMidterm1Sol[1] - 1 IMPORTANT NOTE These...

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