Unformatted text preview: of A and b . (Hint: Remember that the minimum distance of a vector from a linear subspace is along the line that is along the line that is perpendicular to that subspace.) 3. Consider the matrix A = 1 0 1 − 2 1 0 1 2 5 . (a) What is the rank of the matrix A ? (b) Write the matrix in the form A = k ∑ j =1 u ( j )( v ( j ) ) T , where k is the rank of A . (c) Write explicitly the projection matrix onto the span of the columns of A . 4. Consider the linear mapping R 3 → R 3 , x 7→ v × x, where v is a ﬁxed vector in R 3 and “ × ” is the cross product in R 3 . (a) Find a matrix A ∈ R 3 × 3 representing the linear operation. (b) Describe the null space and the range of this matrix. What is the range of the matrix?...
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 Spring '10
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 Linear Algebra, Data Mining, projection matrix, 1 2 5 1 j, mapping R3 R3

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