Three different 2×2 matrices transform the plane R2 as follows. The matrix A rotates the plane clockwise by 30∘, the mat

[answerhappygod]

Three Different 2 2 Matrices Transform The Plane R2 As Follows The Matrix A Rotates The Plane Clockwise By 30 The Mat 1 (207.3 KiB) Viewed 36 times

Three different 2×2 matrices transform the plane R2 as follows. The matrix A rotates the plane clockwise by 30∘, the matrix B projects elements of the plane onto the line x+y=0, and the matrix C shears the plane horizontally by a factor of 0.5. Here are illustrations of these transformations: A:R2→R2 B:R2→R2 C:R2→R2 A. Write down the matrix A in explicit form, i.e. by specifying its components. What are the dimensions of the four fundamental subspaces associated with A ? B. Write down the matrix B in explicit form. What are the dimensions of the four fundamental subspaces associated with B ? C. Write down the matrix C in explicit form. What are the dimensions of the four fundamental subspaces associated with C ? D. Suppose you apply the transformation A, then the transformation B, and then the transformation C to the plane. Write down the explicit form of the matrix that corresponds to applying these transformations in this order, and specify the dimensions of the four fundamental subspaces