Evaluate the following determinant: 1&4&9 4&9&16 9&16&25 - Vidyadip

Question

Evaluate the following determinant:
$\begin{vmatrix}1&4&9\\4&9&16\\9&16&25 \end{vmatrix}$

✓

Answer

Let $\triangle$ be the determinant.
$\triangle=\begin{vmatrix}1&4&9\\4&9&16\\9&16&25 \end{vmatrix}$
Applying $R_3 → R_3 - R_2$, we get
$\Rightarrow\triangle=\begin{vmatrix}1&4&9-4\\4&9&16-9\\9&16&25-16 \end{vmatrix}$
$\Rightarrow\triangle=\begin{vmatrix}1&4&5\\4&9&7\\9&16&9\end{vmatrix}$
$\Rightarrow\triangle=\begin{vmatrix}1&5&5\\4&13&7\\9&25&9 \end{vmatrix}$ [Applying $C_2 → C_1 + C_2$]
$\Rightarrow\triangle=\begin{vmatrix}1&0&0\\4&-7&-13\\9&-20&-36 \end{vmatrix}$ [Applying $C_2 → 5C_1 - C_2$ and $C_3 → 5C_1 - C_3$]
$\Rightarrow\triangle=1(7\times36-13\times20)$
$\Rightarrow\triangle=252-260=-8$

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 "2 Marks Questions" 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

Differentiate the following w.r.t.x: $\log(\cos\text{e}^{\text{x}})$

Determine whether or not the definition of $*$ given below gives a binary operation. In the event that $*$ is not a binary operation give justification of this.
On $Z^+,$ defined $*$ by $a * b = a - b.$
Here, $Z^+$ denotes the set of all non-negative integers.

Find the maximum value of $2{x^3} - 24x + 107$ in the interval [1, 3]. Find the maximum value of the same function in $\left[ { - 3, - 1} \right]$

Let A and B be matrices of orders 3×2 and 2×4 respectively. Write the order of matrix AB.

Compute the indicated product
$\left[\begin{array}{cc} {a} & {b} \\ {-b} & {a} \end{array}\right]\left[\begin{array}{cc} {a} & {-b} \\ {b} & {a} \end{array}\right]$

Prove that if E and F are independent events, then the events E and F' are also independent.

If the tangent to a curve at a point (x, y) is equally inclined to the co-ordinates axes then write the value of $\frac{\text{dy}}{\text{dx}}.$

Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\text{y}\frac{\text{d}^2\text{x}}{\text{dy}^2}=\text{y}^2+1$

If $x\begin{bmatrix}2\\3\end{bmatrix} +y\begin{bmatrix}-1\\1\end{bmatrix} = \begin{bmatrix}10\\5\end{bmatrix}, $find the values of x and y.

If A = {3, 5, 7} and B = {2, 4, 9} and R is a relation given by "is less than", write R as a set ordered pairs.