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)
1)
Find a basis for the column space of A=
2 -4 0 2 1
-1...
1)
Find a basis for the column space of A=
2 -4 0 2 1
-1 2 1 2 3
1 -2 1 4 4
2) Are the following sets vector subspaces of R3?
a) W = {(a,b,|a|) ∈ R3 | a,b ∈ R}
b) V = {(x,y,z) ∈ R3 | x+y+z =0}
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...
Give an example of a matrix, A, whose column space is in
R3 and whose null...
Give an example of a matrix, A, whose column space is in
R3 and whose null space is in R6.
For your matrix above, is it true or false that Col A =
R3? Why or Why not?
The matrix A=
1
0
0
-1
0
0
1
1
1
3x3 matrix
has two...
The matrix A=
1
0
0
-1
0
0
1
1
1
3x3 matrix
has two real eigenvalues, one of multiplicity 11 and one of
multiplicity 22. Find the eigenvalues and a basis of each
eigenspace.
λ1 =..........? has multiplicity 1, with a basis of
.............?
λ2 =..........? has multiplicity 2, with a basis of
.............?
Find two eigenvalues and basis.
Find the transition matrix PB→B0 from the basis B to the basis
B0 where B =...
Find the transition matrix PB→B0 from the basis B to the basis
B0 where B = {(−1, 1, 2),(1, −1, 1),(0, 1, 1)} and B0 = {(2, 1,
1),(2, 0, 1),(1, 1, −1)}. Then apply the matrix to find (~v)B0
where (~v)B = (−3, 2, 9).