Recent content by cubixguy77

Homework Statement Prove that the intersection of any set of ideals of a ring is an ideal. Homework Equations A nonempty subset A of a ring R is an ideal of R if: 1. a - b ε A whenever a, b ε A 2. ra and ar are in A whenever a ε A and r ε R The Attempt at a Solution My guess is...

Homework Statement In an internal combustion engine, air at atmospheric pressure and a temperature of about 20 degrees C is compressed in the cylinder by a piston to (1/8) of its original volume (compression ratio 8.0). Estimate the temperature of the compressed air, assuming the pressure...

Homework Statement Suppose T is a linear operator on a finite dimensional vector space V, such that every subspace of V with dimension dim V-1 is invariant under T. Prove that T is a scalar multiple of the identity operator. The Attempt at a Solution I'm thinking of starting by letting U...

our class was taught such that we're leaving determinants out until the end of the year... so that doesn't tell me a whole heck of a lot if the diagonal is all 0's, what condition would make the matrix invertible (aside from anything having to do with determinants) ?

i'm still unsure of what the diagonal values represent if the diagonals are all 0, what does that tell you about the operator?

Homework Statement Give an example of an operator whose matrix with respect to some basis contains only 0's on the diagonal, but the operator is invertible. The Attempt at a Solution I think the operator will not have an upper-triangular matrix since it would then not be invertible.