The kernel is the set of all points in $\mathbb {R}^5$ such that, multiplying this matrix with them gives the zero vector. Again you can find this in a similar way.

I'm having trouble understanding what it means to find the kernel of a matrix. I have a matrix as follows and I need to determine the kernel. $\begin {bmatrix}2 & 4 & 5 \\ 1 & 2 & ...

Mar 4, 2015 · Finding the kernel of a matrix is equivalent to solving a homogeneous system of linear equations. Surely you have a linear algebra book with applications of solving systems of equations.

Nov 5, 2017 · Finding the kernel of a $4 \times 5$ matrix is a different problem than solving a $4 \times 4$ system of equations with a $4 \times 1$ target vector.

May 31, 2015 · To find the range (image) of T, find the transpose of the matrix first and then reduce the transposed matrix to an echelon form, the remaining non zero matrix becomes the basis for the …

What this is telling you is that you can basically read a basis for the kernel directly from the rref matrix by doing the following: Find the columns that don’t have pivots. You’ll have that many basis vectors, as …

7 The kernel (or null space) of a matrix is the set of all vectors that are mapped to the zero vector by the matrix.

A basis of the image is the columns in the original matrix which correspond to the pivot columns in the row reduced matrix. So presumably the first and second columns of your row reduced matrix are …

Feb 22, 2018 · You can make your answer a little more symmetric (and maybe intuitive, given what the rows of the original matrix are) by replacing the second basis element with $ (0,1,-2,1)^ {\top}$.

However, I don't know how to find the span of a vector column. I'm also confused about how to find the kernel since I think that involves a transformation matrix T but I only have the normal matrix A...