Project Using the Transformation

Problem

T*([a],[b],[d])=([2*a−b+5*d],[−4*a+2*b−10*d]),([4],[4],[1])

Solution

1. Identify the components of the input vector where a=4 b=4 and d=1

2. Substitute these values into the expression for the first component of the transformation.

2*(4)−(4)+5*(1)

3. Simplify the first component calculation.

8−4+5=9

4. Substitute the values into the expression for the second component of the transformation.

−4*(4)+2*(4)−10*(1)

5. Simplify the second component calculation.

−16+8−10=−18

6. Combine the results into the resulting vector.

([9],[−18])

Final Answer

T*([4],[4],[1])=([9],[−18])

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