Assertion -The inverse of the matrix A- 1 1 1- 1 2 3- 1 4 7 - does not exist- Reason- The matrix A is singular

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Standard XII

Mathematics

Singular and Non Singualar Matrices

Assertion :Th...

Question

Assertion :The inverse of the matrix $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 1 1 & 2 & 3 1 & 4 & 7 \end{matrix} ⎤ ⎥ ⎦$ does not exist. Reason: The matrix $A$ is singular

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
$| A | = ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 1 & 2 & 3 1 & 4 & 7 \end{matrix} ∣ ∣ ∣ ∣ = 0$
$A$ is a singular matrix.
Inverse exists iff matrix is non-singular.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Hence, option A.

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Assertion :The inverse of the matrix A=⎡⎢⎣111123147⎤⎥⎦ does not exist. Reason: The matrix A is singular

Assertion :The inverse of the matrix $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 1 1 & 2 & 3 1 & 4 & 7 \end{matrix} ⎤ ⎥ ⎦$ does not exist. Reason: The matrix $A$ is singular