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Let T is a linear transformation. Find the standard matrix of T such that T:R2 → R4 by T(e1) = (3, 1, 3, 1) and T(e2) = (-5, 2, 0, 0) where e1 = (1, 0) and e2 = (0, 1); T:R2 → R4 rotates point as the origin through \(\frac{3\pi}{4}\) radians counter clockwise. T:R2 → R4 Is a vertical shear transformation that maps e1 into e1-2e2 but leaves vector e2 unchanged.

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