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Unformatted text preview: following matrix invertible? a ba cbc 3.246 ±ind a basis of the kernel and image of the matrix. Determine the dimensions of the kernel and image. Determine the rank. Justify your answers. 1 2 3 5 1 4 6 Example (3.331) Let V be the subspace of R 4 de²ned by the equation x 1x 2 + 2x 3 + 4 x 4 = 0 ±ind a linear transformation T from R to R 4 such that ker(T)={0}, im(T)=V. Describe T by its matrix. Give an example of a 5 x 4 matrix A with dim(ker A)=3. Compute dim(im A). Consider the vectors of R 5 , (1,1,0,0,0), (0,0,0,2,2), (1,1,0,1,1), (0,0,1,0,0). Compute the dimension of the subspace V of R spanned by those vectors. Are they linearly independent? Is (1,2,0,0,0) a linear combination of those vectors?...
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 Fall '08
 MOVSHEV
 Linear Algebra, Vectors, Rotation matrix, kernel, R4 deﬁned

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