The matrix product [a b c] ×[x&y&z] ×[p q r] equals :

Question

The matrix product [a b c] ×[x&y&z] ×[p q r] equals : (A) (pqr - abc/xyz) (B) (xyz . pqr /abc) (C) (pqr . abc/xyz) (D) none of these

Tardigrade Admin · Accepted Answer

Matrix product is shown below [a b c] × [x y z]×[p q r] = [ax&ay&az bx&by&bz cx&cy&cz]×[p q r] =[a(xp+yq+zr) b(xp+yq+zr) c(xp+yq+zr)]=(xp+yq+zr)[a b c]

Q. The matrix product
$⎣ ⎡ a b c ⎦ ⎤ \times [x y z] \times ⎣ ⎡ p q r ⎦ ⎤$ equals :

$\frac{pq r - ab c}{x yz}$

$\frac{x yz . pq r}{ab c}$

$\frac{pq r . ab c}{x yz}$

none of these

Matrix product is shown below
$⎣ ⎡ a b c ⎦ ⎤ \times [x y z] \times ⎣ ⎡ p q r ⎦ ⎤ = ⎣ ⎡ a x b x c x a y b y cy a z b z cz ⎦ ⎤ \times ⎣ ⎡ p q r ⎦ ⎤$
$= ⎣ ⎡ a (x p + y q + zr) b (x p + y q + zr) c (x p + y q + zr) ⎦ ⎤ = (x p + y q + zr) ⎣ ⎡ a b c ⎦ ⎤$

Q. The matrix product ⎣⎡​abc​⎦⎤​×[x​y​z​]×⎣⎡​pqr​⎦⎤​ equals :

xyzpqr−abc​

abcxyz.pqr​

xyzpqr.abc​