# B reflects vectors across the vertical axis c

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B reflects vectors across the vertical axis. C orthogonal projection onto the vertical axis, so ( x 1 , x 2 ) (0 , x 2 ) Let M be the linear map that first applies A , then B , and finally C . Find a matrix that represents M in the standard basis for R 2 .

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Name (print) 6 B–3. Let the linear map A : R 3 R 3 be specified by the matrix A := 3 1 0 1 1 - 2 2 1 - 1 . a) Find a basis for the kernel of A . b) Find a basis for the image of A . c) With the above matrix A , is it possible to find an invertible 3 × 3 matrix B so that the matrix AB is invertible?
Name (print) 7 B–4. Say you are given the four data points ( - 1 , 0), (1 , 2), (4 , - 2), and (5 , 3). Find a polynomial p ( x ) of degree at most three that passes through these four points. [Don’t bother to “simplify” your answer.]
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