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Construct the 2 × 2 matrix for the linear transformations R 2 ? R 2 defined...

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Basic Math

Construct the 2 × 2 matrix for the linear transformations R 2 ?R 2 defined by the following compositions. In each case, write downthe matrix of each transformation, then multiply the matrices inthe correct order.

(a) A dilation by a factor of 4, then a reflection across thex-axis.

(b) A counterclockwise rotation through ?/2 , then a dilation bya factor of 1/2 .

(c) A reflection about the line x = y, then a rotation though anangle of ?.

Answer & Explanation Solved by verified expert
4.2 Ratings (685 Votes)
a The matrix representing dilation by a factor of 4 is M 4 0 0 4 The matrix representing reflection across the XAxis is N 1 0 0 1 Hence the matrix representing    See Answer
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