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

Oswaldo Riley

Oswaldo Riley

Answered question


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


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:
Performing row operations, we obtain:
From the row-reduced form, we can see that x3 and x5 are free variables. We can express the null space vectors as:
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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