ok this is about matrices?

Question

ok well metrix a= (in brackets i don't know how to put them up)
a b
c d

metrix b=
e f
g h


now the question-
A does not have an inverse B has an inverse
Column A
ad-bc


Column B
eh-fg


1. the quantity in column a is greater
2. the quantity in column b is greater
3. the two quantities are equal
4. the realationship cannot be determined on the basis of the information supplied.




I am so lost on this question i had no clue how to solve it should i assign numbers to the letter and then work it out. can someone please help me?

Answer 1

Do you know how to calculate determinants of a 2x2 matrix?
Find the determinant of A and B. The problem says that A is not invertible. What does this tell you about A's determinant? B is invertible. What does this tell you about B's determinant?

I hope this helps.

Answer 2

the 2 quantities are teh determinants of teh 2 matrices. Since matrix a has no inverse then the determinant = 0, but matrix b has an inverse so its determinant eh-fg is non-zero but can be positive or negative. The only thing you can say about their relationship is that they are not equal.

Answer 3

Here is part:
The determinant of a is 1 divided by bc - ad.
If bc-ad=0
then the determinant is not defined, and A has no inverse.

We are told that a hasn't inverse. This teels us that bc-ad=0.

The determinant of b is 1 divided by eh-gf = eh -fg. B has an inverse, so the inverse exists, so eh-fg is not equal to zero.

This kind of analysis is probably expected in your response.

Finally, I suggest answer 4.

Answer 4

A does not have an inverse.
This means A is a singular matrix, and its determinant is 0.
ad-bc=0
ad=bc

Answer 5

the answer is 4 ( it is #25 for KNHS)