LINEAR ALGEBRA (Math 211)

**HW #16** (Due Mon. Dec. 4 )

**1.**
Let *T*_{1} and *T*_{2} be the reflections of
about the lines *y*=0 and
.
How many linear operators can be obtained
from *T*_{1} and *T*_{2} using all possible compositions? Find the matrices of
all of them.

**2.** Find the dimensions and bases for the kernel and for the image of
the following transformations

where
*P*_{2}={P(*x*)= *ax*^{2}+*bx*+*c*} is the space of quadratic polynomials.

**3.** Find a linear transformation *T* from
such that

**4.** A linear operator
has the matrix
with respect to the standard basis for .
Find the matrix of this operator with respect to the basis
,

**5.** A linear operator
has the matrix
with respect to the standard basis for
.
Find the matrix of this operator with respect to the basis
,
,
.