Proving an equation using Properties of Determinants

AI Thread Summary
The discussion revolves around proving a specific equation involving determinants without expansion. Participants are sharing methods to approach the proof, emphasizing the use of properties of determinants. One user expresses a desire to verify their answer and seeks confirmation from others. The conversation includes requests for simpler methods to understand the proof. Overall, the focus is on collaborative problem-solving regarding determinant properties.
harshakantha
Messages
41
Reaction score
0
Hello guys I've asked to prove following equation on determinants, here it is;

Using the properties of determinants & without expanding prove that,

see attachment,

I need to verify my answer can some one tell me whether is this correct or not?:smile:
 

Attachments

  • pic1.png
    pic1.png
    13 KB · Views: 521
Physics news on Phys.org
Right, and btw, nice answer .I'd do by the easy determinant way
 
jaumzaum said:
Right, and btw, nice answer .I'd do by the easy determinant way

So why don't u tell me the easyest way??:wink:
 
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
Back
Top