The matrix - 1 1 1- 1 1 1- 1 1 1 - has

The correct option is B no inverseLet A=[ 1 amp; 1 amp; 1; 1 amp; 1 amp; 1; 1 amp; 1 amp; 1 ] |A|=0 So, A^ 1 cannot exist. ...

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Standard XII

Mathematics

Adjoint of a Matrix

The matrix ...

Question

The matrix $⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} 1 & 1 & 1 1 & 1 & 1 1 & 1 & 1 \end{matrix} ⎫ ⎪ ⎬ ⎪ ⎭$ has

one inverse

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two inverse

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no inverse

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cannot be said

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Solution

The correct option is B no inverse
Let $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 1 1 & 1 & 1 1 & 1 & 1 \end{matrix} ⎤ ⎥ ⎦$
$| A | = 0$
So, $A^{- 1}$ cannot exist.

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Similar questions

Q. The rank of the matrix

A = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} 1 & 1 & 1 1 & 1 & 1 1 & 1 & 1 \end{matrix} ⎫ ⎪ ⎬ ⎪ ⎭ i s

We can't find the inverse of a singular matrix because |A|=0.But there should be an inverse for singular matrix as well, right?Is there any way to find the increase ofa singular matrix?

Q. If

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be a matrix such that, inverse of

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, then

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Q. Let

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be a square matrix of order

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such that

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such that

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The matrix ⎧⎪⎨⎪⎩111111111⎫⎪⎬⎪⎭ has

The correct option is B no inverseLet A=⎡⎢⎣111111111⎤⎥⎦|A|=0So,A−1 cannot exist.

The matrix $⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} 1 & 1 & 1 1 & 1 & 1 1 & 1 & 1 \end{matrix} ⎫ ⎪ ⎬ ⎪ ⎭$ has

The correct option is B no inverse
Let $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 1 1 & 1 & 1 1 & 1 & 1 \end{matrix} ⎤ ⎥ ⎦$
$| A | = 0$
So, $A^{- 1}$ cannot exist.