if A=[4 x][x 9] does not have multiplicative inverse then x is
Answers
X should be either 6 or -6.
Given:
Matrix:
To Find:
Value of x if the matrix given does not have a multiplicative inverse.
Solution:
For a square matrix to have a multiplicative inverse it needs to be non-singular which means its determinant needs to be non-zero
So if the determinant of the given matrix is zero it doesn't have a multiplicative inverse.
To find the determinant of a 2x2 square matrix we use:
det(A) = ad - bc
det(A) = (4)9 - xx = 0
36 - = 0
x =
x = 6, -6
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Answer: x should be either 6 or -6 for A to not have a multiplicative inverse.
Given: We are given the matrix
To Find: We need to find the value of x for which the given matrix does not have a multiplicative inverse.
Step-by-Step Explanation: Firstly, we need to see a definition and a property:
Definition of Singular matrix: If determinant of a given matrix is 0, then the matrix is called singular matrix.
Property: A Singular matrix is not invertible.
Step 1: Calculating the determinant of the given matrix:
For a 2x2 matrix, the determinant =
For A matrix, det(A) =
=
Step 2: Solving the equation , will give us the value of x for which the multiplicative inverse of A does not exist.
⇒
⇒ or
⇒ or
To know more about the topic, refer to the links below:
https://brainly.in/question/46885728
https://brainly.in/question/4330169
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