Consider the following two ordered bases of R^2:
B={〈1,−1〉,〈2,−1〉}
C={〈1,1〉,〈1,2〉}.
Find the change of coordinates matrix...
Consider the following two ordered bases of R^2:
B={〈1,−1〉,〈2,−1〉}
C={〈1,1〉,〈1,2〉}.
Find the change of coordinates matrix from the basis B to the
basis C.
PC←B=?
Find the change of coordinates matrix from the basis C to the
basis B.
PB←C=?
Let B = {(1, 3), (?2, ?2)} and B' = {(?12, 0), (?4, 4)} be bases...
Let B = {(1, 3), (?2, ?2)} and B' = {(?12, 0), (?4, 4)} be bases
for R2, and
let A =
3
2
0
4
be the matrix for T: R2 ? R2 relative to B.
(a) Find the transition matrix P from B' to B. P =
(b) Use the matrices P and A to find [v]B and [T(v)]B, where
[v]B' = [1 ?5]T. [v]B = [T(v)]B =
(c) Find P?1 and A' (the matrix for T relative...
Find the dimensions of the null space and the column
space of the matrix (1,-1,-3,4,0), (-1,1,3,-4,1)
Find the dimensions of the null space and the column
space of the matrix (1,-1,-3,4,0), (-1,1,3,-4,1)
Let B = {(1, 2), (−1, −1)} and B' = {(−4, 1), (0, 2)} be bases...
Let B = {(1, 2), (−1, −1)} and B' = {(−4, 1), (0, 2)} be bases
for R2, and let A = −1 2 1 0 be the matrix for T: R2 → R2 relative
to B. (a) Find the transition matrix P from B' to B. P =
(b) Use the matrices P and A to find [v]B and [T(v)]B , where
[v]B' = [−3 1]T. [v]B = [T(v)]B =
(c) Find P inverse−1 and A' (the matrix for...
Consider the following matrix A and its reduced row-echelon
form:
Find the dimensions of row(A), null(A),...
Consider the following matrix A and its reduced row-echelon
form:
Find the dimensions of row(A), null(A), and col(A), and give a
basis for each of them.
A= ( < 0, 0, 0,1 > , < 0, 0, 0, 3 >, < 3, 0, -3,
-2> , < 6, 0, -6, -9 > , < -3, -5, 13 , -2 >,
<-6, -10, 26, -8 > )
rref = ( < 1, 0 ,0, 0 >, < 3, 0, 0, 0...