This video covers a quick way to extract the null space or kernel of a matrix.

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The objective to solve this is assuming you can perform reduced row echelon form already. If you do not know how to perform RREF, watch this video: https://jjthetutor.com/echelon-forms-ef-ref-rref-the-difference-between-echelon-reduced-echelon-reduced-row-echelon/

Once you have the matrix in RREF form, it is as easy as changing the sign of a few numbers in order to pull out the set of vectors that span the null space, which is also called the Kernel or a hyper plane.

Matrix AB=0 – The null space can also be put into a matrix that will product with the original matrix to equal the zero vector or matrix.

View more examples via https://www.youtube.com/watch?v=J5u4fMEHojE&feature=emb_title

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