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Mathematics

Algebra

Easy

Question

If $left square bracket table attributes columnalign left left columnspacing 1em rowspacing 4 pt end attributes row 1 1 row 0 1 end table right square bracket left square bracket table attributes columnalign left left columnspacing 1em rowspacing 4 pt end attributes row 1 2 row 0 1 end table right square bracket left square bracket table attributes columnalign left left columnspacing 1em rowspacing 4 pt end attributes row 1 3 row 0 1 end table right square bracket horizontal ellipsis horizontal ellipsis. left square bracket table attributes columnalign center center columnspacing 1em rowspacing 4 pt end attributes row 1 cell n minus 1 end cell row 0 1 end table right square bracket equals left square bracket table attributes columnalign center center columnspacing 1em rowspacing 4 pt end attributes row 1 78 row 0 1 end table right square bracket$ then the inverse of $left square bracket table attributes columnalign left left columnspacing 1em rowspacing 4 pt end attributes row 1 n row 0 1 end table right square bracket$ is

$[\begin{array}{cc} 1 & 0 \\ 12 & 1 \end{array}]$
$[\begin{array}{cc} 1 & 2 \\ 13 & 1 \end{array}]$
$[\begin{array}{cc} 1 & - 12 \\ 0 & 1 \end{array}]$
$[\begin{array}{cc} 1 & - 13 \\ 0 & 1 \end{array}]$

The correct answer is: $left square bracket table attributes columnalign center center columnspacing 1em rowspacing 4 pt end attributes row 1 cell negative 13 end cell row 0 1 end table right square bracket$

$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em rowspacing 3 pt end attributes row blank cell left square bracket table attributes columnalign left left columnspacing 1em rowspacing 4 pt end attributes row 1 1 row 0 1 end table right square bracket left square bracket table attributes columnalign left left columnspacing 1em rowspacing 4 pt end attributes row 1 2 row 0 1 end table right square bracket left square bracket table attributes columnalign left left columnspacing 1em rowspacing 4 pt end attributes row 1 3 row 0 1 end table right square bracket midline horizontal ellipsis midline horizontal ellipsis left square bracket table attributes columnalign center center columnspacing 1em rowspacing 4 pt end attributes row 1 cell n minus 1 end cell row 0 1 end table right square bracket equals left square bracket table attributes columnalign left left columnspacing 1em rowspacing 4 pt end attributes row 1 78 row 0 1 end table right square bracket end cell row blank cell not stretchy rightwards double arrow left square bracket table attributes columnalign center center columnspacing 1em rowspacing 4 pt end attributes row 1 cell 1 plus 2 plus 3 plus horizontal ellipsis plus n minus 1 end cell row 0 1 end table right square bracket equals left square bracket table attributes columnalign center center columnspacing 1em rowspacing 4 pt end attributes row 1 78 row 0 1 end table right square bracket end cell row blank cell not stretchy rightwards double arrow 1 plus 2 plus 3 plus horizontal ellipsis horizontal ellipsis plus left parenthesis n minus 1 right parenthesis equals 78 end cell row blank cell not stretchy rightwards double arrow fraction numerator n left parenthesis n minus 2 right parenthesis over denominator 2 end fraction equals 78 end cell row blank cell not stretchy rightwards double arrow straight n equals 13 end cell row blank cell text Now inverse of end text left square bracket table attributes columnalign left left columnspacing 1em rowspacing 4 pt end attributes row 1 n row 0 1 end table right square bracket text i.e. end text left square bracket table attributes columnalign center center columnspacing 1em rowspacing 4 pt end attributes row 1 13 row 0 1 end table right square bracket text is end text left square bracket table attributes columnalign center center columnspacing 1em rowspacing 4 pt end attributes row 1 cell negative 13 end cell row 0 1 end table right square bracket text Ans. end text end cell end table$

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