Probably easier for some of you than it was for me, but I thought it was a fairly fun one:
Theorem: 3=4
Proof:
Suppose:
a + b = c
This can also be written as:
4a - 3a + 4b - 3b = 4c - 3c
After reorganizing:
4a + 4b - 4c = 3a + 3b - 3c
Take the constants out of the brackets:
4 * (a+b-c) = 3 * (a+b-c)
Remove the same term left and right:
4 = 3
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Solve for t: 3/4 t=-4
What is the answer to 3/4 t=-4 ?
Trying to understand my kids’ method of math. Reading the question in the title my brain automatically thinks:
4 x 3/4 = 3
But my kids are using a tape diagram method where they draw it out and are getting 5 and 1/3.
Who’s right?
Apologies if you saw the other post. I made a mistake in writing the equations down.
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T:R4 to R4 satisfies T3 + 3T2 = 4I. S = T4 +3T2 -4I.
S is :
one one but not onto.
onto but not one one
invertible
noninvertible
my answer : S is non invertible
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Applying Cayley Hamilton, eigenvalues of T is 1,-2,-2.
When we look at S, eigenvalue 1 -> 1+3-4 = 0,
S has a 0 eigenvalue. S is singular. Thus S cannot be one-one or onto or invertible.
But the answer key answer is one one but not onto..
When dimension of domain and codomain are the same, doesn't one one imply onto?
Another question is T is from dimension 4. But I only have 3. Does that imply one eigenvalue was 0 and was hastily cancelled from the characteristic polynomial?