Given the matrix (4 x) has no inverse, find x
( 2 -5)
To check if a matrix has an inverse, we need to calculate its determinant. If the determinant is equal to zero, then the matrix does not have an inverse.
The given matrix is:
(4 x)
(2 -5)
The determinant is calculated as follows:
det = (4)(-5) - (2)(x) = -20 - 2x
We are told that the matrix has no inverse, so the determinant must be equal to zero:
-20 - 2x = 0
Adding 20 to both sides of the equation:
-2x = 20
Dividing both sides by -2:
x = -10
Therefore, x is equal to -10.
To determine the value of x, let's find the determinant of the given matrix. If the determinant is 0, then the matrix does not have an inverse.
The given matrix is:
[4 x]
[2 -5]
To find the determinant of a 2x2 matrix:
det = (a * d) - (b * c)
In this case, a = 4, b = x, c = 2, and d = -5.
det = (4 * -5) - (x * 2)
det = -20 - 2x
Since the determinant is equal to zero, we can set det = 0 and solve for x:
-20 - 2x = 0
Adding 20 to both sides:
-2x = 20
Dividing both sides by -2:
x = -10
Therefore, the value of x is -10.
To determine the value of x in the matrix (4 x; 2 -5), we first need to check if the matrix has an inverse.
A matrix has an inverse if and only if its determinant is non-zero. Therefore, we need to find the determinant of the given matrix.
The determinant is calculated by multiplying the values on the main diagonal (from top left to bottom right) and subtracting the product of the values on the other diagonal (from top right to bottom left).
For the matrix (4 x; 2 -5), the determinant is:
det = (4 * -5) - (x * 2)
det = -20 - 2x
Since the given matrix has no inverse, the determinant must be zero (det = 0).
Therefore, we can solve for x by setting the determinant equation to zero and solving for x:
-20 - 2x = 0
-2x = 20
x = -20/2
x = -10
So, the value of x in the matrix (4 x; 2 -5) is -10.