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  • Can someone help me with this, - Matrices and Determinants - JEE Main-2

Let and

  If B is the inverse of matrix  A , then \alpha is

  • Option 1)

    2

  • Option 2)

    -1

  • Option 3)

    -2

  • Option 4)

    5

 

Answers (1)

As we learnt in 

Inverse of a matrix -

 A^{-1}=\frac{1}{\left | A \right |}\cdot adjA

-

 

 

A= \begin{bmatrix} 1 & -1 &1 \\ 2& 1 &-3 \\ 1&1 &1 \end{bmatrix}

10(B)= \begin{bmatrix} 4 & 2 &2 \\ -5& 0 &\alpha \\ 1&-2 &3 \end{bmatrix}

and B is the inverse of A.

\left | A \right |= 4+ 1\times 5 +1\times1= 10

B= \frac{adj (A)}{\left | A \right |}= \frac{adj (A)}{10}

So 10 B= adj (A)

Now adj (A) = \begin{bmatrix} 4 &-5 &1 \\ 2& 0 &-2 \\ 2& 5 &3 \end{bmatrix}^{T}= \begin{bmatrix} 4 &2 &2 \\ -5& 0 &5 \\ 1& -2 &3 \end{bmatrix}

\therefore \alpha = 5


Option 1)

2

Incorrect answer

Option 2)

-1

Incorrect answer

Option 3)

-2

Incorrect answer

Option 4)

5

Correct answer

Posted by

Vakul

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