Find a basis for and the dimension of the R 3 subspace W = span{ [-3,4,-3],[-1,2

Question

Find a basis for and the dimension of theR3 subspace
W = span{ [-3,4,-3],[-1,2,-3],[-4,6,-6],[5,-8,9],[7,-10,13] }.
4.1 First enter your basis for W as a set ofR3 row vectors where each row vector isentered as a list.
A basis for W =
4.1 First enter your basis for W as a set ofR3 row vectors where each row vector isentered as a list.
A basis for W =
4.1 First enter your basis for W as a set ofR3 row vectors where each row vector isentered as a list.
A basis for W =
W = span{ [-3,4,-3],[-1,2,-3],[-4,6,-6],[5,-8,9],[7,-10,13] }.

Explanation / Answer

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Response Details: QuestionDetails: 4.1 First enter your basis for W as a set ofR3 row vectors where each row vector isentered as a list.
A basis for W = (-3,4,3),(-1,2,-3),(7,-10,13)

4.1 First enter your basis for W as a set ofR3 row vectors where each row vector isentered as a list.
A basis for W = (-3,4,3),(-1,2,-3),(7,-10,13)

4.2
dim(W) = 3....THREE
4.2
dim(W) = 3....THREE
W = span{ [-3,4,-3],[-1,2,-3],[-4,6,-6],[5,-8,9],[7,-10,13] }.
W=              
V1    V2    V3   V4    V5
-3    -1    -4   5    7
4    2    6   -8    -10
-3    -3    -6   9    13
NR1=-R1/3…..NR2=R2+4R1/3….NR3=R3-R1              
1    0.333333333   1.333333333    -1.666666667   -2.333333333
0    0.666666667   0.666666667    -1.333333333   -0.666666667
0    -2    -2   4    6
NR1=R1-R2/2….NR2=1.5R2….NR3=R3+3R2              
1    0    1   -1    -2
0    1    1   -2    -1
0    0    0   0    4
THERE IS NO ALL ZEROS ROW
SO WE NEED 3 INDEPENDENT VECTORS TO FORM BASIS
SO WE CAN TAKE V1,V2,V5 AS THE BASIS
DIMENSION IS 3

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