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Let T: R R* be a linear transformation defined by T X y Z W = -2x+3y-z+w x+4y+3z-3w x-7y-2z+2w 11y + 5z-5w (a) Find

Let T: R R* be a linear transformation defined by T X y Z W = -2x+3y-z+w x+4y+3z-3w x-7y-2z+2w 11y + 5z-5w (a) Find the matrix representing Twith respect to the standard basis of R. (b) Find the rank and nullity of this transformation. (c) Find the null space for the matrix of this transformation.

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SOLUTION a To find the matrix representing T with respect to the standard basis of R4 we need to apply the transformation T to each basis vector 1 0 0 ... blur-text-image

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