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**Unformatted text preview: **T ( rA ) = ( rA ) ± 1 1 ² = r ³ A ± 1 1 ²´ , and this follows from the associative property of matrix and scalar multiplication. 3. (3 points) Suppose you know that a transformation T : R 2 → R 2 does the following things T ± 1 ² = ±-2 5 ² , T ± 1 1 ² = ±-1 1 ² . 1 Find the matrix representation A T of T . The matrix representation of T is given by A T = ± T ± 1 ² T ± 1 ²² . We know the ﬁrst column, but we need to determine the second. T ± 1 ² = T ³± 1 1 ²-± 1 ²´ = T ± 1 1 ²-T ± 1 ² = ± 1-4 ² , where we used the linearity of T for the second equality. This gives A T = ±-2 1 5-4 ² 2...

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