Q5. Let S and T be linear transformations from R to R defined as follows: S(x,...
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Q5. Let S and T be linear transformations from R³ to R³ defined as follows: S(x, y, z) = (3x + 5y + z, -2x + y - z, x-z) and T(x, y, z) = (x - y, y-z,z - x). α Compute the associated matrices [S]a, [T]a, [S + T]a, [SOT] and [7−¹]a if T-¹ exists, where a is the standard basis of R³. Q5. Let S and T be linear transformations from R³ to R³ defined as follows: S(x, y, z) = (3x + 5y + z, -2x + y - z, x-z) and T(x, y, z) = (x - y, y-z,z - x). α Compute the associated matrices [S]a, [T]a, [S + T]a, [SOT] and [7−¹]a if T-¹ exists, where a is the standard basis of R³.
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