If A - - 1 4 0- 2 5 0- 3 6 0 - and B - - 3 2 1- 1 2 3- 4 5 6 - and C - - 3 2 1- 1 2 3- 7 8 9 - Then evaluate matrix AB - BC

Here, AB=[ 1 amp; 4 amp; 0; 2 amp; 5 amp; 0; 3 amp; 6 amp; 0 ][ 3 amp; 2 amp; 1; 1 amp; 2 amp; 3; 4 amp; 5 amp; 6 ] ⇒ AB ...

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Adjoint of a Matrix

If A = [ 1 ...

Question

If $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 4 & 0 2 & 5 & 0 3 & 6 & 0 \end{matrix} ⎤ ⎥ ⎦$ and $B = ⎡ ⎢ ⎣ \begin{matrix} 3 & 2 & 1 1 & 2 & 3 4 & 5 & 6 \end{matrix} ⎤ ⎥ ⎦$ and $C = ⎡ ⎢ ⎣ \begin{matrix} 3 & 2 & 1 1 & 2 & 3 7 & 8 & 9 \end{matrix} ⎤ ⎥ ⎦$ , Then evaluate matrix $A B - B C$

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A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 4 & 0 2 & 5 & 0 3 & 6 & 0 \end{matrix} ⎤ ⎥ ⎦

B = ⎡ ⎢ ⎣ \begin{matrix} 3 & 2 & 1 1 & 2 & 3 4 & 5 & 6 \end{matrix} ⎤ ⎥ ⎦

C = ⎡ ⎢ ⎣ \begin{matrix} 3 & 2 & 1 1 & 2 & 3 7 & 8 & 9 \end{matrix} ⎤ ⎥ ⎦

A B - B C

Evaluate If a + b + c = 15 and $a^{2} + b^{2} + c^{2}$ = 125 , find ab + bc + ca

∣ ∣ ∣ ∣ ∣ \begin{matrix} {- a}^{2} a b a c \end{matrix} \begin{matrix} a b {- b}^{2} b c \end{matrix} \begin{matrix} a c b c {- c}^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ = λ a^{2} b^{2} c^{2}

λ

∣ ∣ ∣ ∣ ∣ \begin{matrix} - b c & b^{2} + b c & c^{2} + b c a^{2} + a c & - a c & c^{2} + a c a^{2} a b & b^{2} + a b & - a b \end{matrix} ∣ ∣ ∣ ∣ ∣

⎡ ⎢ ⎣ \begin{matrix} 0 & c & - b - c & o & a b & - a & 0 \end{matrix} ⎤ ⎥ ⎦

⎡ ⎢ ⎣ \begin{matrix} a^{2} & a b & a c a b & b^{2} & b c a c & b c & c^{2} \end{matrix} ⎤ ⎥ ⎦

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