There are an infinite number of possibilities for T.
For example: or or
Clearly, this only makes sense for a multiple choice question, where there is only one right answer.
The question is: Which of the following matrices, when substitued for T, satisfies the matrix equation
I know that the answer is the matrix but how do you obtain it without guessing/checking the other choices they had? I mean you can't divide both sides by T like any other equation, so I'm stuck..
Since T maps a 2-vector to a 2-vector it must be a 2 by 2 matrix- you can write it as and then the equation becomes
.
That is, you have two equations to solve for four unknown numbers. That is, as others have told you,
is NOT "the" solution- there are an infinite number of solutions. a= 0, b=1, c= -1, d= 0 do satisfy -3(0)+ 5(1)= 5 and -3(1)+ 5(0)= -3 but, for example, a= -5/3, b= 0, c= 0, d= 3/5 also satisfy those equations so
also satisfies the given matrix equation.
Hi everyone,
This is a practice ACT type question--all of the choices that were included consisted of different variations of 0s and 1s in the 2x2 matrix. So I guess they wanted us to guess and check? I guess I was hoping for a more algebraic way to solve it than by substitution of their choices and seeing which one worked..