Solving Matrix Equations: k Values and Matrix Multiplication

[dagg3r]

hi all just got stuck on these questions on matrices just wondering if anyone can help me out thanks


1. For which values of k is the folowing equation satisfied?

|3-k 5 |
= 0
|4 4-k |

its all in a matrix. I am thinking it is the determinant =0 so
(3-k)(4-k) - 20 = 0

12-7k-k^2 - 20 = 0
-k^2-7k-44=0
then we solve for k? that's out ans?

2. IF A is a matrix or order 2x1, B is 2x3 and C is 3x3 which of the folowing is defined?
a) ABC
b) AT B ( a is transposed * B)
c) BCT + AT (B*Ctransposed + Atransposed)

well i know a) cannot be defined since when you multiply matrices must be the order ie 2x1 * 1x3 etc but won't work

b) can be defined

c) confused since adding matrices not sure how that works.

please reply

thanks

 

[VietDao29]

Question 1:
The question askes for what k that make Det(A) = 0. A is the matrix the problem gives.
Yes. That's correct, but it should read : k^2 -7k - 8 = 0.
Question 2:
a, and b you got it right. For c, A + B is defined iff they have the same dimensions (same number of rows and columns).
Viet Dao,

 

[AKG]

This part is right:

(3-k)(4-k) - 20 = 0

but from there, you said:

12-7k-k^2 - 20 = 0
-k^2-7k-44=0

which is wrong. The mistakes are in red. For the second question, part c), do you know how to add matrices, and what rules there are for adding matrices? Matrices must have the same dimension to be added.

EDIT : Sorry, I see VietDao has already said pretty much what I've said. However, he gave you the equation for part 1, but I'm adding some information by telling you where the mistakes are, so hopefully this helps too.