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

Algebra ->  Matrices-and-determiminant -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Let A=%28matrix%282%2C2%2C2%2C-1%2C4%2C3%29%29 and B=%28matrix%281%2C2%2C3%2C1%29%29

Part a
Part b
Part c



a)

4BA Start with the given product

4%28matrix%281%2C2%2C3%2C1%29%29%28matrix%282%2C2%2C2%2C-1%2C4%2C3%29%29 Plug in matrices A and B


%28matrix%281%2C2%2C4%2A3%2C4%2A1%29%29%28matrix%282%2C2%2C2%2C-1%2C4%2C3%29%29 Multiply the scalar number 4 by every entry in matrix A



%28matrix%281%2C2%2C12%2C4%29%29%28matrix%282%2C2%2C2%2C-1%2C4%2C3%29%29 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
%28matrix%281%2C2%2Ca%2Cb%29%29%28matrix%282%2C2%2Cc%2Cd%2Ce%2Cf%29%29
We can multiply them like this
%28matrix%281%2C2%2Ca%2Ac%2Bb%2Ae%2Ca%2Ad%2Bb%2Af%29%29 which will result in a 1x2 matrix


So for the matrices

%28matrix%281%2C2%2C12%2C4%29%29%28matrix%282%2C2%2C2%2C-1%2C4%2C3%29%29

They can be multiplied like this:

%28matrix%281%2C2%2C12%2A2%2B4%2A4%2C12%2A-1%2B4%2A3%29%29

Multiply

%28matrix%281%2C2%2C24%2B16%2C-12%2B12%29%29

which adds to

%28matrix%281%2C2%2C40%2C0%29%29



b)

B%5E2 Start with the given expression

B%2AB Expand

%28matrix%281%2C2%2C3%2C1%29%29%28matrix%281%2C2%2C3%2C1%29%29 Expand

Since the columns of B do not equal the rows of B, B%5E2 is not defined. So in order to perform powers of matrices, the matrix needs to be square




c)



A%2B2B Start with the given expression


%28matrix%282%2C2%2C2%2C-1%2C4%2C3%29%29%2B2%28matrix%281%2C2%2C3%2C1%29%29 Plug in the given matrices


Since B does not have a second row, A%2B2B is not defined (remember, when you add two matrices, they need to be the same size)