Find an explicit description of Nul A by listing vectors that span the null spac

Oswaldo Riley

Oswaldo Riley

Answered question

2023-03-31

I need to find a unique description of Nul A, namely by listing the vectors that measure the null space
A=[154310121000000]

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Answer & Explanation

Chana Garner

Chana Garner

Beginner2023-04-01Added 4 answers

To find the null space of the matrix A=[154310121000000], we need to solve the equation A𝐱=0, where 𝐱 is a vector in the null space of A.
Setting up the augmented matrix and performing row reduction, we have:
[15431|001210|000000|0]
Performing row operations, we obtain:
[10621|001210|000000|0]
From the row-reduced form, we can see that x3 and x5 are free variables. We can express the null space vectors as:
𝐱=[6s2t2ststs]
where s and t are parameters.
In order to describe the null space, we can write it as the span of the following vectors:
Nul A=Span{[62101],[21010]}
Therefore, the null space of matrix A is described by the set of vectors:
Nul A={[62101],[21010]}

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