Solve for the unknowns given that the following is a singular matrix (1 2)
x x-3
In order for a matrix to be singular, its determinant must be zero.
The determinant of the given matrix is:
(1 * (x-3)) - (2 * x)
= x - 3 - 2x
= -x - 3
To make the matrix singular, we set the determinant equal to zero and solve for x:
-x - 3 = 0
-x = 3
x = -3
Therefore, the unknown x is equal to -3 when the given matrix is singular.
To determine the unknowns, we need to find the values of x that make the matrix singular. A matrix is considered singular if its determinant is equal to zero.
Let's calculate the determinant of the given matrix:
| 1 2 |
| x x-3 |
The determinant is calculated as (1*(x-3)) - (2*x), which simplifies to:
(x-3) - 2x
x - 3 - 2x
-x - 3
For this matrix to be singular, the determinant must be equal to zero:
-x - 3 = 0
To solve for x, we can isolate the variable:
-x = 3
Multiplying both sides by -1:
x = -3
Thus, the unknown value x is -3.