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1. Find a matrix A so that A | y for all z, y, z E R. What are the dimensions of A? 2y +2z (The dimensions of an m x n matrix are m × n.) for all R2. Find a matrix A so that T-LA (that is. Τ(x) = Ax for all fe R2). and all vectorsR2. Do not assume any properties of the dot product, beyond the definition. (Hint write Aa21 a22and x 2. Let T: IR2R2 be the function so that T() is the vector obtained by reflecting across the y-axis, 3. Let A be a 3 x 2 matrix. Show directly from the definition that A(ki) - k(Afor al scalars k e R a11 a12 and compute A(kr) and k(A) directly from the definition.)

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This is a problem in linear algebra. The problem requires the use of matrix product and linear transformation.2 2 3 2 2乙yt 3 I

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