Evaluate - - - 3 -1 -2- 0 0 -1- 3 -5 0 -

[ | [ 3 amp; 1 amp; 2; 0 amp; 0 amp; 1; 3 amp; 5 amp; 0 ]| =3( 0 ( 1 ) ( 5 ) #160; ) ( 1 ) ( 0 3( 1 ) #160; ...

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Standard XII

Mathematics

Determinant

Evaluate : ...

Question

Evaluate :
$∣ ∣ ∣ ∣ \begin{matrix} 3 & - 1 & - 2 0 & 0 & - 1 3 & - 5 & 0 \end{matrix} ∣ ∣ ∣ ∣$

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Solution

$\begin{matrix} ∣ ∣ ∣ ∣ \begin{matrix} 3 & - 1 & - 2 0 & 0 & - 1 3 & - 5 & 0 \end{matrix} ∣ ∣ ∣ ∣ = 3 (0 - (- 1) (- 5)) - (- 1) (0 - 3 (- 1)) + (- 2) (0 (- 5) - 0 (3)) = 3 (- 5) - (- 3) + 0 = - 15 + 3 = - 12 \end{matrix}$

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Evaluate the determinants

(i) $∣ ∣ ∣ ∣ \begin{matrix} 3 & - 1 & - 2 0 & 0 & - 1 3 & - 5 & 0 \end{matrix} ∣ ∣ ∣ ∣$

(ii) $∣ ∣ ∣ ∣ \begin{matrix} 0 & 1 & 2 - 1 & 0 & - 3 - 2 & 3 & 0 \end{matrix} ∣ ∣ ∣ ∣$

(iii) $∣ ∣ ∣ ∣ \begin{matrix} 3 & - 4 & 5 1 & 1 & - 2 2 & 3 & 1 \end{matrix} ∣ ∣ ∣ ∣$

(iv) $∣ ∣ ∣ ∣ \begin{matrix} 2 & - 1 & - 2 0 & 2 & - 1 3 & - 5 & 0 \end{matrix} ∣ ∣ ∣ ∣$

Q. Find the inverse of

⎡ ⎢ ⎣ \begin{matrix} 3 & - 1 & - 2 2 & 0 & - 1 3 & - 5 & 0 \end{matrix} ⎤ ⎥ ⎦

by using elementary row transformations.

Evaluate (i) $(1^{3} + 2^{3} + 3^{3})^{\frac{1}{2}}$ (ii) ${[5 {(8^{\frac{1}{3}} + 27^{\frac{1}{3}})}^{3}]}^{\frac{1}{4}}$ (iii) $\frac{2^{0} + 7^{0}}{5^{0}}$ (iv) ${[(16)^{\frac{1}{2}}]}^{\frac{1}{2}}$

Q. Using elementary row transformation find the inverse of the matrix A =

⎡ ⎢ ⎣ \begin{matrix} 3 & - 1 & - 2 2 & 0 & - 1 3 & - 5 & 0 \end{matrix} ⎤ ⎥ ⎦

Q. Evaluate the determinant :-

∣ ∣ ∣ ∣ \begin{matrix} 3 & - 1 & - 2 0 & 0 & - 1 3 & - 5 & 0 \end{matrix} ∣ ∣ ∣ ∣

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Evaluate : ∣∣ ∣∣3−1−200−13−50∣∣ ∣∣

∣∣ ∣∣3−1−200−13−50∣∣ ∣∣=3(0−(−1)(−5))−(−1)(0−3(−1))+(−2)(0(−5)−0(3))=3(−5)−(−3)+0=−15+3=−12

Evaluate :
$∣ ∣ ∣ ∣ \begin{matrix} 3 & - 1 & - 2 0 & 0 & - 1 3 & - 5 & 0 \end{matrix} ∣ ∣ ∣ ∣$

$\begin{matrix} ∣ ∣ ∣ ∣ \begin{matrix} 3 & - 1 & - 2 0 & 0 & - 1 3 & - 5 & 0 \end{matrix} ∣ ∣ ∣ ∣ = 3 (0 - (- 1) (- 5)) - (- 1) (0 - 3 (- 1)) + (- 2) (0 (- 5) - 0 (3)) = 3 (- 5) - (- 3) + 0 = - 15 + 3 = - 12 \end{matrix}$