Evaluate 1&x&y 1&x+y&y 1&x&x+y - Vidyadip

Question

Evaluate $\begin{vmatrix}1&\text{x}&\text{y}\\1&\text{x}+\text{y}&\text{y}\\1&\text{x}&\text{x+y}\end{vmatrix}$

✓

Answer

$\triangle=\begin{vmatrix}1&\text{x}&\text{y}\\1&\text{x}+\text{y}&\text{y}\\1&\text{x}&\text{x+y}\end{vmatrix}$
Applying $R_2 → R_2 - R_1$ and $R_3 → R_3 - R_1$, we have:
$\triangle=\begin{vmatrix}1&\text{x}&\text{y}\\0&\text{y}&0\\0&0&\text{x}\end{vmatrix}$
Expanding along $C_1$, we have:
$\triangle$ = 1(xy - 0) = xy

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

Find the unit vector in the direction of vector $\overrightarrow{\text{PQ}}$ where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively.

construct a 3 × 4 matrix, whose elements are given by:
$\text a_{\text {ij}}=2{\text{i}}-{\text{j}} $

For any two vectors $\vec{\text{a}}$ and $\vec{\text{b}},$ find $\vec{\text{a}}.\big(\vec{\text{b}}\times\vec{\text{a}}\big).$

If $\text{A}=\begin{bmatrix}0&-1&2\\4&3&-4\end{bmatrix}$ and $\text{B}=\begin{bmatrix}4&0\\1&3\\2&6\end{bmatrix},$ then verify that $(\text{A}')'=\text{A}.$

Integrate the function $\frac{\log x}{(1+\log x)^2}$ with respect to $x$.

For the principal values, evaluate the following:
$\sin^{-1}\Big(-\frac{\sqrt3}{2}\Big)+\text{cosec}^{-1}\Big(-\frac{2}{\sqrt3}\Big)$

Differentiate the following w.r.t.x: $\frac{\text{e}^\text{x}}{\sin\text{x}}$

Find the principal values:
$\tan^{-1}(-1)$

Evaluate the following integrals:
$\int\frac{\cos\sqrt{\text{x}}}{\sqrt{\text{x}}}\text{ dx}$

Fatima and John appear in an interview for two vacancies for the same post. The probability of Fatima's selection is $\frac{1}{7}$ and that of John's selection is $\frac{1}{5}$. What is the probability that,
None of them will be selected?