For the matrix A below, find a nonzero vector in Nul A and a nonzero vector in Col A. A=\begin{bmatrix}2&3&5&-9\\-8&-9&-11&21\\4&-3&-17&27\end{bmatrix} Find a nonzero vector in Nul A. A=\begin{bmatrix}-3\\2\\0\\1\end{bmatrix}

mattgondek4 2021-06-13 Answered
For the matrix A below, find a nonzero vector in Nul A and a nonzero vector in Col A.
A=[2359891121431727]
Find a nonzero vector in Nul A.
A=[3201]
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Expert Answer

Willie
Answered 2021-06-14 Author has 95 answers
Consider the following matrix,
A=[2359891121431727]
Find a non-zero vector in Nul A.
Use row reduced method.
A=[13/25/29/2891121431727]R112R1
[13/25/29/203915092745]R2R2+8R1,R3R34R1
[13/25/29/2039150000]R3R3+3R2
[102301350000]R1R112R2
The matrix has 2 pivot columns and 2 free columns.
Then, AX=0
[102301350000][x1x2x3x4]=[000]
x12x3+3x4=0x1=2x33x4
x2+3x35x4=0x2=3x3+5x4
So, the general solution is,
{x1=2x33x4x2=3x3+5x4x3 and x4 are free variables
Then, a vector parametric solution is,
[x1x2x3x4]=[2x33x43x3+5x4x3x4]
=[2x33x3x3x4]+[3x45x40x4]
=[2310]x3+[3501]x4
Therefore, the required non-zero vectors in Nul A are,
(2,3,1,0),(3,5,0,1)
Find a non zero vector in Col A
observe the equation (1), the first two columns of the matrix
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