Using Cofactors of elements of second row, evaluate = 5&3&8 2&0&1… - Vidyadip

Question

Using Cofactors of elements of second row, evaluate $\triangle=\begin{vmatrix}5&3&8\\2&0&1\\1&2&3\end{vmatrix}.$

✓

Answer

The given determinant is $\begin{vmatrix}5&3&8\\2&0&1\\1&2&3\end{vmatrix}.$
we have:
M₂₁ $=\begin{vmatrix}3&8\\2&3\end{vmatrix}=9-16=-7$
$\therefore$ A₂₁ = cofactor of a₂₁ = (-1)²⁺¹M₂₁ = 7
M₂₂ $=\begin{vmatrix}5&8\\1&3\end{vmatrix}=15-8=7$
$\therefore$ A₂₂ = cofactor of a₂₂ = (-1)²⁺² M₂₂ = 7
M₂₃ $=\begin{vmatrix}5&3\\1&2\end{vmatrix}=10-3=7$
$\therefore$ A₂₃ = cofactor of a₂₂ = (-1)²⁺³ M₂₃= -7
We know that $\triangle$ is equal to the sum of the product of the elements of the second row with their corresponding cofactor.
$\therefore\triangle$ = a₂₁A₂₁ + a₂₂A₂₂+ a₂₃A₂₃= 2(7) + 0(7) + 1(-7) = 14 - 7 = 7

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks" from DETERMINANTS→DETERMINANTS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Evaluate the following integrals:
$\int\frac{1}{\sqrt{1-\text{x}^2}(\sin^{-1}\text{x})^2}\text{dx}$

If $|\vec{\text{a}}|=\text{a}$ and $\big|\vec{\text{b}}\big|=\text{b},$ prove that $\Big(\frac{\vec{\text{a}}}{\text{a}^2}-\frac{\vec{\text{b}}}{\text{b}^2}\Big)^2=\Big(\frac{\vec{\text{a}}-\vec{\text{b}}}{\text{ab}}\Big)^2.$

Prove the following results:
$\sin^{-1}\frac{63}{65}=\sin^{-1}\frac{5}{13}+\cos^{-1}\frac{3}{5}$

A factory has two machines A and B. Past records show that the machine A produced 60% of the items of output and machine B produced 40% of the items. Further 2% of the items produced by machine A were defective and 1% produced by machine B were defective. If an item is drawn at random, what is the probability that it is defective?

Let the function f : R → R be defined by f(x) = cosx, ∀ x ∈ R. Show that f is neither one-one nor onto.

Dot product of a vector with vectore $\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}},2\hat{\text{i}}+\hat{\text{j}}-3\hat{\text{k}}$ and $\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$ are respectively 4, 0 and 2. Find the vector.

Write a value of $\int\text{e}^{\text{x}}(\sin\text{x}+\cos\text{x})\text{dx}$

In the following, find the value of the constant k so that the given function is continuous at the indicated point:
$\text{f(x)}=\begin{cases}\text{k}(\text{x}^2-2\text{x}),&\text{if}\text{ x}<0\\\cos\text{x},&\text{if}\text{ x}\geq0\end{cases}\text{at x} = 0$

Reduce the equation of the following planes to intercept from and find the intercepts on the coordinate axes:
2x - y + z = 5

Evaluate the following intregals:
$\int\frac{1}{\cos2\text{x}+3\sin^2\text{x}}\ \text{dx}$