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Maths-

General

Easy

Question

$open vertical bar table attributes columnalign center center center columnspacing 1em end attributes row 1 w cell w squared end cell row w cell w squared end cell 1 row cell w squared end cell 1 w end table close vertical bar equals$

$- 1$
1
0
2

hint Hint:

To find the determinant of the given matrix first we will make some adjustments, for column 1 if we will add the three column we will get all the elements of column 1 equal then we take it common, as all the elements of column 1 is 1 now so by looking at the theorem we can find value of the determinant.

The correct answer is: 0

$space space space space open vertical bar table attributes columnalign center center center columnspacing 1em end attributes row 1 w cell w squared end cell row w cell w squared end cell 1 row cell w squared end cell 1 w end table close vertical bar equals open vertical bar table row cell 1 plus w plus w squared end cell w cell w squared end cell row cell 1 plus w plus w squared end cell cell w squared end cell 1 row cell 1 plus w plus w squared end cell 1 w end table close vertical bar space space space space space space space open square brackets C subscript 1 rightwards arrow C subscript 1 plus C subscript 2 plus C subscript 3 close square brackets equals open parentheses 1 plus w plus w squared close parentheses open vertical bar table row 1 w cell w squared end cell row 1 cell w squared end cell 1 row 1 1 w end table close vertical bar space space space space space space space space equals open parentheses 1 plus w plus w squared close parentheses cross times 0 space space space space space space space space space space space space space open square brackets C o l l i n e a r i t y close square brackets equals 0$

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