Proving $beginvmatrixa&b&c\b&c&a\c&a&bendvmatrix=-(a+b+c)(a^2+b^2+c^2-ab-bc-ca)$Calculate $beginVmatrix1&2\2&4endVmatrix$Compute the determinant $beginvmatrix sin x & cos x \ -sin y & cos y endvmatrix$ using the Sarrus' ruleProving a determinant equalityTo show: $beginvmatrix -bc & b^2+bc & c^2+bc\ a^2+ac & -ac & c^2+ac \ a^2+ab & b^2+ab & -ab endvmatrix= (ab+bc+ca)^3$Find the value of the determinant $scriptsize beginvmatrix 8-x & -10 & 6 \ 8 & -9-x & -1 \ 16 & -15 & 9-x endvmatrix$Given $beginvmatrix p & q & r \ s & t & u \ v & w & x endvmatrix = -3$, find $beginvmatrixp&2q&5r+4p\s&2t&5u+4s\v&2w&5x+4vendvmatrix$.$beginvmatrix 1 & a &bc \ 1& b & ac\ 1&c & ab endvmatrix=beginvmatrix 1 & a &a^2 \ 1& b&b^2 \ 1& b & c^2 endvmatrix$Prove that $beginvmatrix xa&yb&zc\ yc&za&xb\ zb&xc&ya\ endvmatrix=xyzbeginvmatrix a&b&c\ c&a&b\ b&c&a\ endvmatrix$ if $x+y+z=0$Prove the equality: $beginvmatrix -2a &a+b &a+c \ b+a&-2b &b+c \ c+a&c+b &-2c endvmatrix = 4(a+b)(b+c)(c+a)$Determinant of beginvmatrix -2a &a+b &a+c \ b+a& -2b &b+c \ c+a&c+b & -2c endvmatrix
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Proving $beginvmatrixa&b&c\b&c&a\c&a&bendvmatrix=-(a+b+c)(a^2+b^2+c^2-ab-bc-ca)$
Calculate $beginVmatrix1&2\2&4endVmatrix$Compute the determinant $beginvmatrix sin x & cos x \ -sin y & cos y endvmatrix$ using the Sarrus' ruleProving a determinant equalityTo show: $beginvmatrix -bc & b^2+bc & c^2+bc\ a^2+ac & -ac & c^2+ac \ a^2+ab & b^2+ab & -ab endvmatrix= (ab+bc+ca)^3$Find the value of the determinant $scriptsize beginvmatrix 8-x & -10 & 6 \ 8 & -9-x & -1 \ 16 & -15 & 9-x endvmatrix$Given $beginvmatrix p & q & r \ s & t & u \ v & w & x endvmatrix = -3$, find $beginvmatrixp&2q&5r+4p\s&2t&5u+4s\v&2w&5x+4vendvmatrix$.$beginvmatrix 1 & a &bc \ 1& b & ac\ 1&c & ab endvmatrix=beginvmatrix 1 & a &a^2 \ 1& b&b^2 \ 1& b & c^2 endvmatrix$Prove that $beginvmatrix xa&yb&zc\ yc&za&xb\ zb&xc&ya\ endvmatrix=xyzbeginvmatrix a&b&c\ c&a&b\ b&c&a\ endvmatrix$ if $x+y+z=0$Prove the equality: $beginvmatrix -2a &a+b &a+c \ b+a&-2b &b+c \ c+a&c+b &-2c endvmatrix = 4(a+b)(b+c)(c+a)$Determinant of beginvmatrix -2a &a+b &a+c \ b+a& -2b &b+c \ c+a&c+b & -2c endvmatrix
$begingroup$
Prove:$$beginvmatrixa&b&c\b&c&a\c&a&bendvmatrix=-(a+b+c)(a^2+b^2+c^2-ab-bc-ca)$$
I tried to use the Laplace expansion, but it seems useless.
matrices determinant
$endgroup$
add a comment |
$begingroup$
Prove:$$beginvmatrixa&b&c\b&c&a\c&a&bendvmatrix=-(a+b+c)(a^2+b^2+c^2-ab-bc-ca)$$
I tried to use the Laplace expansion, but it seems useless.
matrices determinant
$endgroup$
add a comment |
$begingroup$
Prove:$$beginvmatrixa&b&c\b&c&a\c&a&bendvmatrix=-(a+b+c)(a^2+b^2+c^2-ab-bc-ca)$$
I tried to use the Laplace expansion, but it seems useless.
matrices determinant
$endgroup$
Prove:$$beginvmatrixa&b&c\b&c&a\c&a&bendvmatrix=-(a+b+c)(a^2+b^2+c^2-ab-bc-ca)$$
I tried to use the Laplace expansion, but it seems useless.
matrices determinant
matrices determinant
edited Mar 17 at 12:54
Rodrigo de Azevedo
13.2k41960
13.2k41960
asked Mar 17 at 12:06
DavidDavid
644
644
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1 Answer
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$begingroup$
Hint:
$C_1'=C_1+C_2+C_3$
$$beginvmatrixa&b&c\b&c&a\c&a&bendvmatrix$$
$$=beginvmatrixa+b+c&b&c\b+c+a&c&a\c+a+b&a&bendvmatrix$$
$$=(a+b+c)beginvmatrix1&b&c\1&c&a\1&a&bendvmatrix$$
Now either expand or
use $R_2'=R_2-R_1, R_3'=R_3-R_1$
$endgroup$
add a comment |
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1 Answer
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$begingroup$
Hint:
$C_1'=C_1+C_2+C_3$
$$beginvmatrixa&b&c\b&c&a\c&a&bendvmatrix$$
$$=beginvmatrixa+b+c&b&c\b+c+a&c&a\c+a+b&a&bendvmatrix$$
$$=(a+b+c)beginvmatrix1&b&c\1&c&a\1&a&bendvmatrix$$
Now either expand or
use $R_2'=R_2-R_1, R_3'=R_3-R_1$
$endgroup$
add a comment |
$begingroup$
Hint:
$C_1'=C_1+C_2+C_3$
$$beginvmatrixa&b&c\b&c&a\c&a&bendvmatrix$$
$$=beginvmatrixa+b+c&b&c\b+c+a&c&a\c+a+b&a&bendvmatrix$$
$$=(a+b+c)beginvmatrix1&b&c\1&c&a\1&a&bendvmatrix$$
Now either expand or
use $R_2'=R_2-R_1, R_3'=R_3-R_1$
$endgroup$
add a comment |
$begingroup$
Hint:
$C_1'=C_1+C_2+C_3$
$$beginvmatrixa&b&c\b&c&a\c&a&bendvmatrix$$
$$=beginvmatrixa+b+c&b&c\b+c+a&c&a\c+a+b&a&bendvmatrix$$
$$=(a+b+c)beginvmatrix1&b&c\1&c&a\1&a&bendvmatrix$$
Now either expand or
use $R_2'=R_2-R_1, R_3'=R_3-R_1$
$endgroup$
Hint:
$C_1'=C_1+C_2+C_3$
$$beginvmatrixa&b&c\b&c&a\c&a&bendvmatrix$$
$$=beginvmatrixa+b+c&b&c\b+c+a&c&a\c+a+b&a&bendvmatrix$$
$$=(a+b+c)beginvmatrix1&b&c\1&c&a\1&a&bendvmatrix$$
Now either expand or
use $R_2'=R_2-R_1, R_3'=R_3-R_1$
answered Mar 17 at 12:08
lab bhattacharjeelab bhattacharjee
227k15158278
227k15158278
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