I'm confused on this style of proof. How does this prove that c1 = c2 = c3 = 0 for ALL x in R, when you only selected a few values of x for the example? There are infinitely many more possible values of x to be chosen? If that makes sense ...
Stating that the linear combination is true for all x, implies solving a system of equations. In this example we need three example values to get c1, c2 and c3.
what you're trying to do here is to use values of x that will guarantee a value of 0. so if you were to use, let's say, x = 5, then you'd solve nothing since you'd have c1, c2, and c3 in the equation and nothing gets cancelled out. but after working through the problem, you'll see that any value of x will make sure the equation is true since the coefficients are 0 and 0 multiplied by anything is 0. but to get to that point, you need to use x values that cancels out the other coefficients, like it was shown in the video.
Sir for your kind knowledge that term becomes zero because C2 is zero, not because cosπ is zero. See lecture carefully and then comment your fucking observations.
![How to Determine if a Set of Vectors is Linearly Independent [Passing Linear Algebra]](/img/1.gif)
Thank you so much... I was looking everywhere for an explanation online and I found the best one here, right on your channel!
Not a proof by any measure..you have to verify for any general value of x over the set of real numbers
What will happen if we put h(x)= tanx in the set of these given functions.
Is it L.D. or L.I. ?
Cos pi =-1.
thank you
I'm confused on this style of proof. How does this prove that c1 = c2 = c3 = 0 for ALL x in R, when you only selected a few values of x for the example? There are infinitely many more possible values of x to be chosen? If that makes sense ...
If the linear combination of those functions is the zero function for all x hence it must be true for some x
Stating that the linear combination is true for all x, implies solving a system of equations. In this example we need three example values to get c1, c2 and c3.
Pls how does sin pie/2 equals to 1??
sin pie/2 is equal to 1, how did you end up here not knowing that?
Lookup the unit circle on youtube. This is not the video for you haha
hey can u solve it with the help of matrix??
Helo sir sinx, cosx, sinx-cosx which mean linearly depent or lineraly independent sir pls clarification
they are linearly dependent since you can write third function as combination of first two. sinx-cosx=a.sinx+b.cosx where a=1 and b=-1.
@@saurabhrana2534 linearly independent varatha sir
@@gunaharish5701 varatha means?
Great man.....
👍
What if we take other values of x
what you're trying to do here is to use values of x that will guarantee a value of 0. so if you were to use, let's say, x = 5, then you'd solve nothing since you'd have c1, c2, and c3 in the equation and nothing gets cancelled out. but after working through the problem, you'll see that any value of x will make sure the equation is true since the coefficients are 0 and 0 multiplied by anything is 0. but to get to that point, you need to use x values that cancels out the other coefficients, like it was shown in the video.
Fun problem :)
Brother cos(π)= -1
-1xo=0
Sir for your kind knowledge I wanna tell you that cos pie is not equal to zero. It's -1 . Practice first then upload.
Sir for your kind knowledge that term becomes zero because C2 is zero, not because cosπ is zero.
See lecture carefully and then comment your fucking observations.
no, but c2 is 0, and he proved that earlier. and (-1)×(0) = 0 so that's why he said that c2 times cos(pi) is 0.
The value of cosπ=-1 . U have put wrong value.
bhai cos(pi)=-1. you are misleading.