Reference no: EM132688106
Question 1: Find the eigenvalues and bases for the eigenspace of the matrix
![242_figure.jpg](https://secure.expertsmind.com/CMSImages/242_figure.jpg)
Question 2: Suppose that T: R3 → R3 is a linear transformation so that
![897_figure1.jpg](https://secure.expertsmind.com/CMSImages/897_figure1.jpg)
(a) Find ![1134_figure2.jpg](https://secure.expertsmind.com/CMSImages/1134_figure2.jpg)
(b) Find ![2489_figure3.jpg](https://secure.expertsmind.com/CMSImages/2489_figure3.jpg)
Question 3: Let T: P2 → P2 by
T(ax2 + bx + c) = (4b + a)x2 + (c - a)x + (3c - b - a);
α the standard basis for P2; β the basis consisting of
2x2 + 3x, x2+5, x+7; v=2x2+7x - 3
(a) Find [T]aa where a is the standard basis for P2.
(b) Find the change of basis matrix from a to β.
(c) Find the change of basis matrix from β to a.
(d) Find [T]ββ
(e) Find [v]β
(f) Find [T(v)]β.
(g) Find T(v).
Question 4: Determine whether the given matrix A (3×3) is diagonalizable and, if it is, give a diagonal matrix similar to A as well as a matrix P and its inverse so that P-1 AP is this diagonal matrix.
![598_figure4.jpg](https://secure.expertsmind.com/CMSImages/598_figure4.jpg)