Determine the null space of each of the following matrices: begin{bmatrix}1 & 1&-1&2 2 & 2&-3&1-1&-1&0&-5 end{bmatrix}

Jaya Legge 2021-02-21 Answered
Determine the null space of each of the following matrices:
[111222311105]
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Expert Answer

Talisha
Answered 2021-02-22 Author has 93 answers
Step 1
Solve the given system Ax=0 using Gauss-jordan reduction method.
Step 2
Obtain the augmented matrix as shown below:
[1112|02231|01105|0][1112|00013|01105|0](R2R22R1)
[1112|00013|00013|0](R3R3+R1)
[1112|00013|00000|0](R3R3R2)
[1105|00013|00000|0](R1R1R2)
[1105|00013|00000|0](R2R2)
Step 3
Then,
[110500130000][x1x2x3]=0
x1+x2+5x4=0
x3+3x4=0
Here the free variables are x2,x4 thus , on setting x2=α,x4=β we have , x1=α5β,x3=3β
Thus , the null space N(A) contain all the vectors of the form:
(α5β,α,3β,β)T=α(1.1.0.0)T+β(5,0,3,1)T,α,βR
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Jeffrey Jordon
Answered 2022-01-27 Author has 2064 answers

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