SOLUTION: <pre> Given that P = │ 2 4 │ │-9 1 │ and Q = │1 - 1│ │3 -2│, find PQ + 2Q.</pre>

Algebra ->  Test -> SOLUTION: <pre> Given that P = │ 2 4 │ │-9 1 │ and Q = │1 - 1│ │3 -2│, find PQ + 2Q.</pre>       Log On


   

Question 1210332: 
Given that

P = │ 2  4 │
    │-9  1 │         

and
 
Q  = │1  - 1│
     │3   -2│,

find PQ + 2Q.
Found 3 solutions by mccravyedwin, MathLover1, math_tutor2020:
Answer by mccravyedwin(408) About Me  (Show Source):
You can put this solution on YOUR website!

find PQ + 2Q.

P=%28matrix%282%2C2%2C2%2C4%2C-9%2C1%29%29

Q=%28matrix%282%2C2%2C1%2C-1%2C3%2C-2%29%29

%22%22=%22%22

%22%22%2B%22%22%28matrix%282%2C2%2C2%281%29%2C2%28-1%29%2C2%283%29%2C2%28-2%29%29%29

%28matrix%282%2C2%2C2%2B12%2C-2-8%2C+-9%2B3%2C9-2%29%29%29%22%22%2B%22%22%28matrix%282%2C2%2C2%2C-2%2C6%2C-4%29%29

%28matrix%282%2C2%2C14%2C-10%2C+-6%2C7%29%29%29%22%22%2B%22%22%28matrix%282%2C2%2C2%2C-2%2C6%2C-4%29%29

%28matrix%282%2C2%2C14%2B2%2C-10-2%2C-6%2B6%2C7-4%29%29

%28matrix%282%2C2%2C16%2C-12%2C0%2C3%29%29

Edwin

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Given that
P = matrix%282%2C2%2C2%2C4%2C-9%2C1%29
and
Q = matrix%282%2C2%2C1%2C-1%2C3%2C-2%29

find PQ + 2Q.

if P = matrix%282%2C2%2C2%2C4%2C-9%2C1%29

than
2P= 2%2A%28matrix%282%2C2%2C2%2C4%2C-9%2C1%29%29= matrix%282%2C2%2C4%2C8%2C-18%2C2%29

if Q = matrix%282%2C2%2C1%2C-1%2C3%2C-2%29
than 2Q=2%28matrix%282%2C2%2C1%2C-1%2C3%2C-2%29%29=matrix%282%2C2%2C2%2C-2%2C6%2C-4%29

PQ + 2Q= matrix%282%2C2%2C4%2C8%2C-18%2C2%29+matrix%282%2C2%2C2%2C-2%2C6%2C-4%29=matrix%282%2C2%2C6%2C+6%2C+-12%2C+-2%29




Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

There are two routes you can follow.
  1. Compute PQ and 2Q separately. Then add them together. This is what tutor Edwin has done.
  2. Note that Q is present in both PQ and 2Q, so we can factor it out using the distributive property. PQ + 2Q = PQ + 2*I*Q = (P+2I)*Q. Where I is the identity matrix. Be careful to remember that matrix multiplication is NOT commutative.
I should elaborate on the 2nd method. The identity matrix is needed so that we can validly add the stuff in the parenthesis.

The expression P+2 wouldn't make much sense to add a matrix to a scalar.
But P+2I makes more sense because it's the expression %28matrix%282%2C2%2C2%2C4%2C-9%2C1%29%29%2B2%2A%28matrix%282%2C2%2C1%2C0%2C0%2C1%29%29 i.e. %28matrix%282%2C2%2C2%2C4%2C-9%2C1%29%29%2B%28matrix%282%2C2%2C2%2C0%2C0%2C2%29%29
I'll let the student handle the scratch work for the second method if they follow that route.

You can use online calculators to verify that Edwin has the correct answer.
The tutor MathLover1 mistakenly computed 2P instead of PQ, so that explains why she arrived at an incorrect answer.