Three different 2 x 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 4 B: R² R² CER² 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 Cin explicit form. What are the dimensions of the four fundamental subspaces associated with C?

Three different 2 x 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 4 B: R² R² CER² 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 Cin explicit form. What are the dimensions of the four fundamental subspaces associated with C?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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