Linear Algebra:
Find the orthogonal projection of u3=[48,-12,108] onto the plane
spanned by u1= [2,7,2] and...
Linear Algebra:
Find the orthogonal projection of u3=[48,-12,108] onto the plane
spanned by u1= [2,7,2] and u2=[5,35,15].
Answer Choices: [15,3,-3] [35,23,-34] [5,1,3] [-22,28,38]
[24,21,-6] [24,0,6] [34,14,18] [21,22,-11] [57,12,27]
[39,37,15]
3. Find the linear transformation T : R2 → R2 described
geometrically by “first rotate coun-...
3. Find the linear transformation T : R2 → R2 described
geometrically by “first rotate coun- terclockwise by 60◦, then
reflect across the line y = x, then scale vectors by a factor of
5”. Is this linear transformation invertible? If so, find the
matrix of the inverse transformation.
Find the matrix for a linear map T: R4 ->
R3 given by T([a, b, c,...
Find the matrix for a linear map T: R4 ->
R3 given by T([a, b, c, d]) = [-c+d, a-b+4c, 3b+2d].
3.) Find the linear transformation T : R2 to R2 described
geometrically by "first rotate counter-clockwise...
3.) Find the linear transformation T : R2 to R2 described
geometrically by "first rotate counter-clockwise by 60 degrees,
then reflect across the line y = x, then scale vectors by a factor
of 5". Is this linear transformation invertible? If so, find the
matrix of the inverse transformation.
Find the matrix A in the linear transformation y =
Ax,where a point x = [x1,x2]^T...
Find the matrix A in the linear transformation y =
Ax,where a point x = [x1,x2]^T is projected on the x2 axis.That
is,a point x = [x1,x2]^T is projected on to [0,x2]^T . Is A an
orthogonal matrix ?I any case,find the eigen values and eigen
vectors of A .
Let T be the linear transformation from R2 to R2, that rotates a
vector clockwise by...
Let T be the linear transformation from R2 to R2, that rotates a
vector clockwise by 60◦ about the origin, then reflects it about the
line y = x, and then reflects it about the x-axis.
a) Find the standard matrix of the linear transformation T.
b) Determine if the transformation T is invertible. Give detailed
explanation. If T is invertible, find the standard matrix of the
inverse transformation T−1.
Please show all steps clearly so I can follow your...
Problem 2. (20 pts.) show that T is a linear transformation by
finding a matrix that...
Problem 2. (20 pts.) show that T is a linear transformation by
finding a matrix that implements the mapping. Note that x1, x2, ...
are not vectors but are entries in vectors. (a) T(x1, x2, x3, x4) =
(0, x1 + x2, x2 + x3, x3 + x4) (b) T(x1, x2, x3, x4) = 2x1 + 3x3 −
4x4 (T : R 4 → R)
Problem 3. (20 pts.) Which of the following statements are true
about the transformation matrix...