LINEAR ALGEBRA (Math 211)
HW #14 (Due Wed. Nov. 29 )

1. Determine which of the following transformations are into linear and find the corresponding matrices with respect to the standard basis for .

 (a) T(x,y,z)=(x,0,z) (d) T(x,y,z)=(x+y,2x+z,3x+y-z) (b) T(x,y,z)=(1,z,x-y) (e) T(x,y,z)=(3x+5y,3x+5y,3x+5y) (c) T(x,y,z)=(x,y,1/z) (f) T(x,y,z)=(x-1,y,z+1)

2. Find the matrices of the following linear transformations from into with respect to the standard bases:
(a) projection along the first coordinate axis;         (b) projection along the second coordinate axis.

3. Find the matrices of the following linear transformations from into with respect to the standard basis for :
(a) reflection about the line 2x-3y=0;         (b) rotation by the angle .

4. Consider the space P4={P(x)= ax4+bx3+cx2+dx+e} of polynomials of degree . Find the matrix of the linear operator with respect to the standard basis x4, x3, x2, x, 1.

5. Let be a linear operator defined by the formula for a given number and any from . Find the matrix of T with respect to the standard basis for .