Asked by jim
                let A=(3     x)
(-2 -3)
if A=A^-1, what is x?
please show work so i can understand
            
        (-2 -3)
if A=A^-1, what is x?
please show work so i can understand
Answers
                    Answered by
            drwls
            
    Is (3 x) a 2 x 1 matrix?
What is the meaning of the second line, (-2 -3)? It just sits there.
Is the A matrix in the first line supposed to operate on (3 x) ?
(3 x) and (-2 -3) cannot be multiplied.
One has ti be a column vector.
    
What is the meaning of the second line, (-2 -3)? It just sits there.
Is the A matrix in the first line supposed to operate on (3 x) ?
(3 x) and (-2 -3) cannot be multiplied.
One has ti be a column vector.
                    Answered by
            MathMate
            
    The second line is probably meant to be the second row of the 2x2 matrix.
I.e. A=
(3 x}
(-2 -3)
If A=A<sup>-1</sup>, then
A<sup>-1</sup>A = I
(3 x} (3 x}
(-2 -3)(-2 -3) = I
Performing the matrix multiplication:
(9-2x 0)
(0 -2x+9) = I
so
9-2x=1
or x=4
Substitute x=4 and redo the matrix multiplication to make sure that the result is a 2x2 identity matrix.
    
I.e. A=
(3 x}
(-2 -3)
If A=A<sup>-1</sup>, then
A<sup>-1</sup>A = I
(3 x} (3 x}
(-2 -3)(-2 -3) = I
Performing the matrix multiplication:
(9-2x 0)
(0 -2x+9) = I
so
9-2x=1
or x=4
Substitute x=4 and redo the matrix multiplication to make sure that the result is a 2x2 identity matrix.
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