SOLUTION: Please help with the following: Let A= 2 -1 4 3 B= [3 1] Perform the following operations if possible: a. 4BA b. B^2 c. A+2B Am I right in the pos

Question 102575: Please help with the following:
Let A= 2 -1
4 3
B= [3 1]
Perform the following operations if possible:
a. 4BA
b. B^2
c. A+2B
Am I right in the possiblity that a and c are not possible?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let and

Part a
Part b
Part c

a)

Start with the given product

Plug in matrices A and B

Multiply the scalar number 4 by every entry in matrix A

Multiply

Now multiply matrices B and A. In order for this to be defined, the number of columns in B needs to be the same as the number of rows in A. Since this is true, BA is defined.

Now if you have two general matrices

We can multiply them like this
which will result in a 1x2 matrix

So for the matrices

They can be multiplied like this:

Multiply

which adds to

b)

Start with the given expression

Expand

Expand

Since the columns of B do not equal the rows of B, is not defined. So in order to perform powers of matrices, the matrix needs to be square

c)

Start with the given expression

Plug in the given matrices

Since B does not have a second row, is not defined (remember, when you add two matrices, they need to be the same size)
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