mat211FinalReview

mat211FinalReview - MAT 211 - Introduction to linear...

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Unformatted text preview: MAT 211 - Introduction to linear algebra, Final Review (1) (1) Compute the determinant of the matrix (2) Determine the all the values of k for which the matrix is invertible. 1 0 0 2 0 0 2 0 2 0 2 0 0 k (2) Find an orthogonal matrix A such that if T is a linear transformation on R 3 defined by T ( x ) = AX then T (1 / √ 2 , 1 / √ 2 , 0) = (1 , , 0). (3) Consider the vectors vectorv 1 = (1 , 2 , 3 , 4) vectorv 2 = (5 , 6 , 7 , 8) vectorv 3 = (4 , 3 , 2 , 1) vectorv 4 = (1 , 1 , 1 , 1) in R 4 . Compute the dimension of span { v 1 ,v 2 ,v 3 ,v 4 } . (4) Find a basis of the subspace of all 3 × 3 matrices formed by all 3 × 3 symmetric matrices. Give the coordinates of the identity and of E = 1 10 20 10 30 20 30 , with respect to that basis. (5) The three transformations below are defined the linear space formed by all 2 × 2 matrices. For each of them, determine whether it linear. If it is, find kernel, image, nullity and rank....
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This note was uploaded on 09/14/2011 for the course MAT 211 taught by Professor Movshev during the Spring '08 term at SUNY Stony Brook.

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mat211FinalReview - MAT 211 - Introduction to linear...

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