Further Matricied

Question 1

Def

Answer 1

Ad-bc
If 0 then singular
No unique solution

Area multiplier

I’d def m is 0 no inverse

Question 2

Det Rules

Det of AB =.?

Answer 2

1) Det of matrix (AB) = Det A x detB
- because scale factor x scale factor
Proof? Show Det full of variables
- and then show that Det one x 2 gives same

Question 3

Det of (KA) where k a constant?

Answer 3

This just k2 Det A

Can just sub in K and see k2 happens

Question 4

I’d Det 0, what is equation of line

Answer 4

Always through origin, all values plotted to this line with no area (Det is 0), and no info so no way of retrieving original points (no inverse)

• map to point (xy) and then compare y with x (divide y with x to find multiplier , this is GRADIENT)

Now have line

Question 5

Inverse of matriculated

Answer 5

Gives I, no matter what order

But if Det is 0 then can’t

Question 6

Long but nice derivation for 2 by 2 matrix inverse what is it acc

Answer 6

1/ Det (swap leading diagonal, and then swap signs on other diagonal !

Question 7

Why is an inverse matrix unique to its original?

Answer 7

This because it don’t matter which way you do it = it just gives same
Show this by just showing a by inverse and inverse by a

And both times can just factor the Det out

Here is as it is commutive

And since Det m is 0 then it is singular and no unique because bare matrices can become that same valuel

But normally only one matricu becomes one inverse

Question 8

Inverse matrix is

Answer 8

Commutative

And unique to one

Question 9

How to prove the inverse of (AB) is B-1A-1

Answer 9

Let inverse of (AB) = x
So that x multiplied AB = I

Now POST MULTIPLY EACH WITH THE RIGHTEST TERM, this gets rid of the thing

Eventually you get x as B-1A-1

Remember if do B then A, need to reverse A then B
Thus B-1A-1