Question

if A=[4 x][x 9] does not have multiplicative inverse then x is

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Answer 1

X should be either 6 or -6.

Given:

Matrix: $\left[\begin{array}{ccc}4&x\\x&9\end{array}\right]$

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 - $x^{2}$ = 0

x = $\sqrt{36}$

x = 6, -6

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Answer 2

Answer: x should be either 6 or -6 for A to not have a multiplicative inverse.

Given: We are given the matrix $\left[\begin{array}{cc}4&x\\x&9\end{array}\right]$

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, $\left[\begin{array}{cc}a&b\\c&d\end{array}\right]$ the determinant = $ad-bc$

For A matrix, det(A) = $4*9-x^2$

                                = $36-x^2$

Step 2: Solving the equation $36-x^2 = 0$ , will give us the value of x for which the multiplicative inverse of A does not exist.

$36-x^2=0$

⇒ $36=x^2$

⇒ $x= \sqrt{36}$ or $-\sqrt{36}$

⇒ $x=6$ or $-6$

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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