Homework SourseDetermine whether the vector u belongs to the null space of
Determine whether the vector u belongs to the null space of the matrix A. u = [2 4 1], A = [-2 3 -8 -3 -3 18] Yes No![Determine whether the vector u belongs to the null space of the matrix A. u = [2 4 1], A = [-2 3 -8 -3 -3 18] Yes NoSolutionA vector u is in the null space of](/WebImages/12/determine-whether-the-vector-u-belongs-to-the-null-space-of-1012116-1761522570-0.webp "Determine whether the vector u belongs to the null space of the matrix A. u = [2 4 1], A = [-2 3 -8 -3 -3 18] Yes NoSolutionA vector u is in the null space of")
Solution
A vector u is in the null space of a matrix A if
Au = 0
So check if multiplying the matrix by the vector is 0 (a zero vector).
If we multiply these two i.e. Au, we will get:
one row and two columns.
We will get in first row and first column = 2*(-2) + 4*3 + 1*(-8) = -4 +12 -8 = 0
We will get in first row and second column = 2*(-3) + 4*(-3) + 1*18 = -6 -12 + 18 = 0
Therefore, it\'s a null vector.
Hence, answer is YES.
