a((1),(4))+b((3),(-1))=((1),(0)) Find a and b

Luciano Webster

Luciano Webster

Answered question

2022-07-19

a ( 1 4 ) + b ( 3 1 ) = ( 1 0 ) Find a and b
I've found the answers to this to be 1 13 and 4 13 through google but just wondering, how would I go about working this through and finding the answer myself?

Answer & Explanation

juicilysv

juicilysv

Beginner2022-07-20Added 17 answers

Multiply the two matrices as shown and you will have following equations:
a + 3 b = 1
4 a b = 0
From (2), we have:
b=4a
Putting in (1), we get:
a+3(4a)=1
this implies,
13a=1
So
a = 1 13
and
b = 4 13
Bruno Thompson

Bruno Thompson

Beginner2022-07-21Added 9 answers

You would set up two equations in the unknowns a,b, by using the fact that vectors are equal if and only if their components are equal. Thus, you get
a+3b=1,and4a−b=0
which I am pretty sure you can solve.

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