Question
Using properties of determinants, prove that
; background:rgba(220,220,220,0.5))
![]( "Click and drag to move")
✓
Answer
Operating R2 ; background:rgba(220,220,220,0.5))
![]( "Click and drag to move")
R2 - 4R1 and R3 ![]()
![]( "Click and drag to move")
R3 -8R1, we get
; background:rgba(220,220,220,0.5))
![]( "Click and drag to move")
Expanding along C2,we get
– x (– 5x2 + 4x2) = x3.
Expanding along C2,we get
– x (– 5x2 + 4x2) = x3.
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
The volume of a cube increases at a constant rate. Prove that the increase in its surface area varies inversely as the length of the side.
Differentiate the following functions with respect to x:
$\text{x}^{\text{x}^2-3}+(\text{x}-3)^{\text{x}^2}$
→$\text{x}^{\text{x}^2-3}+(\text{x}-3)^{\text{x}^2}$
A manufacturing company makes two models A and B of a product. Each piece of model A requires 9 labour hours for fabricating and 1 labour hour for finishing. Each piece of model B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available are 180 and 30 respectively. The company makes a profit of Rs. 8000 on each piece of model A and Rs. 12000 on each piece of model B. How many pieces of model A and model B should be manufactured per week to realise a maximum profit? What is the maximum profit per week?
An oil company has two depots, A and B, with capacities of 7000 litres and 4000 litres respectively. The company is to supply oil to three petrol pumps, D, E, F whose requirements are 4500, 3000 and 3500 litres respectively. The distance (in km) between the depots and petrol pumps is given in the following table:
Assuming that the transportation cost per km is Rs. 1.00 per litre, how should the delivery be scheduled in order that the transportation cost is minimum?
Assuming that the transportation cost per km is Rs. 1.00 per litre, how should the delivery be scheduled in order that the transportation cost is minimum?
Solve the following differential equation:
$\big[\text{x}\sqrt{\text{x}^2+\text{y}^2}-\text{y}^2\big]\text{dx}+\text{xy dy}=0$
→$\big[\text{x}\sqrt{\text{x}^2+\text{y}^2}-\text{y}^2\big]\text{dx}+\text{xy dy}=0$
Evaluate the following integrals:
$\int\limits^{\frac{\pi}{3}}_\frac{\pi}{6}\frac{1}{1+\cot^{\frac{3}{2}}\text{x}}\text{ dx}$
→$\int\limits^{\frac{\pi}{3}}_\frac{\pi}{6}\frac{1}{1+\cot^{\frac{3}{2}}\text{x}}\text{ dx}$
Find $\frac{\text{dy}}{\text{dx}}$
$\text{y}=\frac{(\text{x}^2-1)^3(2\text{x}-1)}{\sqrt{(\text{x}-3)(4\text{x}-1)}}$
→$\text{y}=\frac{(\text{x}^2-1)^3(2\text{x}-1)}{\sqrt{(\text{x}-3)(4\text{x}-1)}}$
Integrate the function $\frac{1}{{\sqrt {8 + 3x - {x^2}} }}$
→Differentiate the following functions with respect to x:
$\sin^{-1}\big(1-2\text{x}^2\big),0<\text{x}<1$
→$\sin^{-1}\big(1-2\text{x}^2\big),0<\text{x}<1$
Use product $\begin{bmatrix}1&-1&2\\0&2&-3\\3&-2&4\end{bmatrix}\begin{bmatrix}-2&0&1\\9&2&-3\\6&1&-2\end{bmatrix}$ to solve the system of equations x + 3z = 9, -x + 2y - 2z = 4, 2x - 3y + 4z = -3.
→