Linear algebra help plooox? (1 Viewer)

[hayabusaboston]

My notes indicate nothing on the reasoning behind this. My lecturer gave us activity page which generates random questions. Can anyone help me with this pls?
Three q's

http://imgur.com/a/WgClW

 

[seanieg89]

What you need to know:

The number of free parameters is the dimension of the solution space.

This is equal to the dimension of the kernel of your linear operator/matrix. (Or complementary to the rank of your linear operator/matrix.)

You can read these things off directly from a row echelon form.

 

[seanieg89]

Second q is correct, and first option is correct for third q.

 

[hayabusaboston]

What you need to know:

The number of free parameters is the dimension of the solution space.

This is equal to the dimension of the kernel of your linear operator/matrix. (Or complementary to the rank of your linear operator/matrix.)

You can read these things off directly from a row echelon form.

So free variables is rank of the matrix? so 5 free variables? or 4? :/

what about the other two?

EDIT: complimentary to rank OH so its 4 yea?

 

[hayabusaboston]

Second q is correct, and first option is correct for third q.

Could you explain reasoning behind 2 and 3 pls?

 

[seanieg89]

So free variables is rank of the matrix? so 5 free variables? or 4? :/

what about the other two?

Try to figure this out yourself, it is just a matter of definitions and you will learn 100x more deciding between the two options yourself.

Reasoning for the others:
2. We want our plane to pass through the origin, because the system is homogeneous. The correct answer is the plane through the origin parallel to the affine solution plane.
3. This is immediate from the definition of matrix multiplication.

 

[seanieg89]

Yes, it's 4.