Express Plane V as Kernel & Image of Matrices A & B | Homework Solution

[Tonyt88]

Homework Statement

Express the plane V in 3 with equation 3x1+4x2+5x3=0 as the kernel of a matrix A and as the image of a matrix B.
{Note: the 1,2, and 3 after the x are subscript}

Homework Equations

The Attempt at a Solution

Would the relevant matrix just be a [3 4 5] with an image of 3?

 

[gammamcc]

Plane V in 3 ? Do you mean in R^3?

You have a lot of room to play with here, since there is not just one single example. Hints:
For the first part, the dimension of the null space is that of a plane (in R^3) and is of dim 2. The dimension of the row space would be 3-dim null space=1.

For the second part, I would try to find two vectors that span the given plane (remember 3rd semester calc with analytic geometry? Remember how to find the normal to a plane and how to get two linearly independent vectors perpendicular to that normal?) . That would give you the col. space of the matrix. As you need three columns, you can take one of the col.'s to be a linear combination of two others you have derived.
Good Luck

 

[HallsofIvy]

Homework Statement

Express the plane V in 3 with equation 3x1+4x2+5x3=0 as the kernel of a matrix A and as the image of a matrix B.
{Note: the 1,2, and 3 after the x are subscript}

Homework Equations

The Attempt at a Solution

Would the relevant matrix just be a [3 4 5] with an image of 3?

Do you understand that you are asked for two matrices, A and B?
You might want to review the definitions of "kernel of a matrix" and "image of a matrix".