Question
Find values of x, if $\left|\begin{array}{ll} {2} & {3} \\ {4} & {5} \end{array}\right|=\left|\begin{array}{cc} {x} & {3} \\ {2 x} & {5} \end{array}\right|$
✓
Answer
We know that determinant of A is calculated as $|A|=\left|\begin{array}{ll} {a} & {b} \\ {c} & {d} \end{array}\right|$ = ad - bc
We have $\left|\begin{array}{cc} {2} & {3} \\ {4} & {5} \end{array}\right|=\left|\begin{array}{cc} {x} & {3} \\ {2 x} & {5} \end{array}\right|$
$\Rightarrow$ 2(5) – 3(4) = x(5) – 3(2x)
$\Rightarrow$ 10 – 12 = 5x – 6x
$\Rightarrow$ -2 = -x
$\Rightarrow$ x = 2
The value of x is 2.
We have $\left|\begin{array}{cc} {2} & {3} \\ {4} & {5} \end{array}\right|=\left|\begin{array}{cc} {x} & {3} \\ {2 x} & {5} \end{array}\right|$
$\Rightarrow$ 2(5) – 3(4) = x(5) – 3(2x)
$\Rightarrow$ 10 – 12 = 5x – 6x
$\Rightarrow$ -2 = -x
$\Rightarrow$ x = 2
The value of x is 2.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
In Fig 10.6 (a square), identify the following vectors.
Coinitial.
Coinitial.
Integrate the function $\frac{1}{\left(x^{2}+1\right)\left(x^{2}+4\right)}$
→Write the vector equation of the plane, passing through the point (a, b, c) and parallel to the plane $\overrightarrow{\text{r}}.(\hat{\text{i}} + \hat{\text{j}} + \hat{\text{k}}) = 2.$
→Find the distance between the planes 2x – y + 2z = 5 and 5x – 2.5y + 5z = 20.
The number of all possible matrices of order $3 \times 3$ with each entry 0 or 1 is
→Evaluate the determinant $\left|\begin{array}{ccc}0 & 1 & 2 \\ -1 & 0 & -3 \\ -2 & 3 & 0\end{array}\right|$
→Show that the relation R in the set Z of integers given by R = {(a, b) : 2 divides a-b} is an equivalence relation.
On which of the following intervals is the function f given by $f(x) = x^{100} + sinx – 1$, decreasing?
→Construct a 2 × 2 matrix, A = $[\text{a}_{\text {ij}}]$, whose elements are given by:
→$\text a_{\text {ij}}=\frac{\text i}{\text j} $
What is the value of the determinant $\begin{vmatrix} 0 & 2 & 0 \\ 2 & 3 & 4 \\ 4 & 5 & 6 \end{vmatrix}?$
→