A- - 1 amp- 5 amp- 2- 3 amp- 1 amp- 4- 2 amp- 2 amp- 3 - -The following elementary nbsp-transformations are applied on the matrix A in the given order- What will be the resultant matrix- -R-2 - R-2 - R-3 -R-1 - R-1 - R-2 -R-3 - R-3 nbsp-2 R-2 - 0 amp- 6 amp- 1- 2 amp- -1 amp- 2- 0 amp- -4 amp- 1 - 0 amp- 6 amp- 2- 2 amp- 1 amp- 1- 0 amp- -4 amp- 1 - 0 amp- 6 amp- 2- 1 amp- 1 amp- 1- 0 amp- -4 amp- 1 - 0 amp- 6 amp- 1- 1 amp- -1 amp- 1- 0 amp- 4 amp- 1 -

The correct option is D [ 0 amp; 6 amp; 1; 1 amp; 1 amp; 1; 0 amp; 4 amp; 1 ] Given matrix, [ 1 amp; 5 amp; 2; 3 amp; 1 amp; ...

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Byju's Answer

Standard XII

Mathematics

Elementary Transformations

A= [ 1 a...

Question

$A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 5 & 2 3 & 1 & 4 2 & 2 & 3 \end{matrix} ⎤ ⎥ ⎦$ .The following elementary transformations are applied on the matrix A in the given order. What will be the resultant matrix?

$⎡ ⎢ ⎣ \begin{matrix} 0 & 6 & 1 2 & - 1 & 2 0 & - 4 & 1 \end{matrix} ⎤ ⎥ ⎦$

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$⎡ ⎢ ⎣ \begin{matrix} 0 & 6 & 1 1 & - 1 & 1 0 & 4 & 1 \end{matrix} ⎤ ⎥ ⎦$

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$⎡ ⎢ ⎣ \begin{matrix} 0 & 6 & 2 2 & 1 & 1 0 & - 4 & 1 \end{matrix} ⎤ ⎥ ⎦$

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$⎡ ⎢ ⎣ \begin{matrix} 0 & 6 & 2 1 & 1 & 1 0 & - 4 & 1 \end{matrix} ⎤ ⎥ ⎦$

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Solution

The correct option is B
$⎡ ⎢ ⎣ \begin{matrix} 0 & 6 & 1 1 & - 1 & 1 0 & 4 & 1 \end{matrix} ⎤ ⎥ ⎦$

Given matrix, $⎡ ⎢ ⎣ \begin{matrix} 1 & 5 & 2 3 & 1 & 4 2 & 2 & 3 \end{matrix} ⎤ ⎥ ⎦$

$R_{2} \to (R_{2} - R_{3}) \Rightarrow ⎡ ⎢ ⎣ \begin{matrix} 1 & 5 & 2 3 - 2 & 1 - 2 & 4 - 3 2 & 2 & 3 \end{matrix} ⎤ ⎥ ⎦$

$\Rightarrow$ $⎡ ⎢ ⎣ \begin{matrix} 1 & 5 & 2 1 & - 1 & 1 2 & 2 & 3 \end{matrix} ⎤ ⎥ ⎦$

$R_{1} \to (R_{1} - R_{2}) \Rightarrow ⎡ ⎢ ⎣ \begin{matrix} 1 - 1 & 5 + 1 & 2 - 1 1 & - 1 & 1 2 & 2 & 3 \end{matrix} ⎤ ⎥ ⎦$

$\Rightarrow$ $⎡ ⎢ ⎣ \begin{matrix} 0 & 6 & 1 1 & - 1 & 1 2 & 2 & 3 \end{matrix} ⎤ ⎥ ⎦$

$R_{3} \to R_{3} - 2 R_{2} \Rightarrow ⎡ ⎢ ⎣ \begin{matrix} 0 & 6 & 1 1 & - 1 & 1 0 & 4 & 1 \end{matrix} ⎤ ⎥ ⎦$

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Similar questions

A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 5 & 2 3 & 1 & 4 2 & 2 & 3 \end{matrix} ⎤ ⎥ ⎦

The following elementary transformations are applied on the matrix A in the given order. The resultant matrix after the following operations

R_{2}

\to

R_{2}

–

R_{3}

R_{1}

\to

R_{1} - R_{2}

R_{3}

\to

R_{3}

– 2

R_{2}

Applying the following transformations will result in on the matrix in order on the matrix in order $⎡ ⎢ ⎣ \begin{matrix} 1 & 5 & 2 3 & 1 & 4 2 & 2 & 3 \end{matrix} ⎤ ⎥ ⎦$

\frac{R_{1}}{r_{1}} + \frac{R_{2}}{r_{2}} + \frac{R_{3}}{r_{3}} =

Q. If in a

△ A B C, r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1}

is equal to
(where

r_{1}, r_{2}

and

r_{3}

are the exradii and

2 s

is the perimeter.)

Q. In determinants, is the following operation allowed on a 3*3 matrix?
R₁ = R₁ + (R₂ * R₃)

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A=⎡⎢⎣152314223⎤⎥⎦ .The following elementary transformations are applied on the matrix A in the given order. What will be the resultant matrix?

$A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 5 & 2 3 & 1 & 4 2 & 2 & 3 \end{matrix} ⎤ ⎥ ⎦$ .The following elementary transformations are applied on the matrix A in the given order. What will be the resultant matrix?