Respuesta :
A matrix B that has V as its nullspace. (c) Multiply A and B is [tex]I (4 by 4 ).[/tex]
[tex]\mathbb{R}^4[/tex]
What is a Nullspace vector?
The null space of A is all the vectors x for which Ax = 0, and it is denoted by null(A). This means that to check to see if a vector x is in the null space we need only to compute Ax and see if it is the zero vector.
- All vectors whose components are equal.
- All vectors whose components add to zero.
- All vectors that are perpendicular to [tex](1,1,0,0)$ and $(1,0,1,1)$.[/tex]
- The column space and the nullspace of (4 by 4 ).
Solution. These bases are not unique.
[tex]- $(1,1,1,1)$.- $(1,-1,0,0),(1,0,-1,0)$, and $(1,0,0,-1)$.- $(1,-1,-1,0)$ and $(1,-1,0,-1)$.[/tex]
- The columns of are a basis of its column space: [tex]$(1,0,0,0),(0,1,0,0)$, $(0,0,1,0)$, and $(0,0,0,1)$.[/tex]The nullspace contains the zero vector only. By convention, the empty set is the basis of such a space.
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