SOLUTION: Find a non-zero 2×2 matrix such that [-9, -3] [18, 6] x [_,_] [_,_] = [0,0] [0,0] FILL IN THE BLANKS

Algebra ->  Matrices-and-determiminant -> SOLUTION: Find a non-zero 2×2 matrix such that [-9, -3] [18, 6] x [_,_] [_,_] = [0,0] [0,0] FILL IN THE BLANKS      Log On


   

Question 1159574: Find a non-zero 2×2 matrix such that
[-9, -3]
[18, 6]
x
[_,_]
[_,_]
=
[0,0]
[0,0]
FILL IN THE BLANKS
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

You are given this matrix equation

    %28matrix%282%2C2%2C+-9%2C-3%2C++18%2C6%29%29 * X = %28matrix%282%2C2%2C+0%2C0%2C++0%2C0%29%29,

where X is 2x2 unknown NON-ZERO matrix to find.


Notice that the given matrix on the left of matrix X has the left column exactly THREE TIMES as its right column.


Therefore, our task is to find the unknown matrix X in such a way that, applied to the left-most matrix as a factor from the right, 

it would produce the zero 2x2-matrix.


It leads to   

    X = %28matrix%282%2C2%2C+1%2C1%2C++-3%2C-3%29%29.      (1)


Now, check it on your own that

    %28matrix%282%2C2%2C+-9%2C-3%2C++18%2C6%29%29 * %28matrix%282%2C2%2C+1%2C1%2C++-3%2C-3%29%29 = %28matrix%282%2C2%2C+0%2C0%2C++0%2C0%29%29.


So,  the matrix  (1)  is your  ANSWER.

Solved.