I think "Just picked some number" means any number for which the then derived equation holds and derived from there: 10beta - 5gamma = 0: it (I haven't proved it ,but I am fairly certain) could be any number, but 1 is "nice" in this case, since it just goes to be 10 * 1 - 5 * 2 = 0. But you could pick any other one and calculate from there: Example: 10beta - 5gamma = 0 -> 10beta = 5gamma; lets pick beta = 15, then that will mean gamma is 10beta = 5gamma | divide both sides by 5 2beta = 1gamma | for beta = 15 2 * 15 = 30 = gamma and then alpha = (-4beta + 5gamma) / -3 = 90 / -3 = -30 (from second row of the matrix) and from the first line of the matrix: alpha + 2beta = 0; check: -30 + 2 * 15 = 0 So we have: alpha[1, -3] + beta[2, 4] + gamma[0, -5] = 0; for alpha = -30, beta=15, gamma=30 check: first row: -30 * 1 + 15 * 2 + 0 = 0 second row: -30 * -3 + 15 * 4 + 30 * -5 = 0 You could also start with different row(like first row where alpha + 2beta + 0gamma = alpha + 2beta = 0, pick a number and go from there) Hope this helps.
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Great Channel Growth Man. I'm the derivative guy.
Great video! Thank you!
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Topic is most clearly explained and presented; big THANK YOUUUUU👍 in China.
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Was going great until 6:38. Why is Beta = 1? What do you mean you "just picked a number"?
I think "Just picked some number" means any number for which the then derived equation holds and derived from there:
10beta - 5gamma = 0:
it (I haven't proved it ,but I am fairly certain) could be any number, but 1 is "nice" in this case, since it just goes to be 10 * 1 - 5 * 2 = 0. But you could pick any other one and calculate from there: Example:
10beta - 5gamma = 0 -> 10beta = 5gamma; lets pick beta = 15, then that will mean gamma is
10beta = 5gamma | divide both sides by 5
2beta = 1gamma | for beta = 15
2 * 15 = 30 = gamma
and then alpha = (-4beta + 5gamma) / -3 = 90 / -3 = -30 (from second row of the matrix)
and from the first line of the matrix: alpha + 2beta = 0; check: -30 + 2 * 15 = 0
So we have:
alpha[1, -3] + beta[2, 4] + gamma[0, -5] = 0; for alpha = -30, beta=15, gamma=30
check:
first row:
-30 * 1 + 15 * 2 + 0 = 0
second row:
-30 * -3 + 15 * 4 + 30 * -5 = 0
You could also start with different row(like first row where alpha + 2beta + 0gamma = alpha + 2beta = 0, pick a number and go from there)
Hope this helps.
Thank you sir👍
For trivial representation all scalar should be equal to zero..
And for nontrivial representation all scalar should not be equal to zero.
Am I right?