Recent content by delgeezee

i know S = { $$1 , x, x^2$$} is linearly dependent set for p2. where $$(a_0, a_1, a_2) = (0,0,0) $$ I wanted to use the Wronskian on { $$1 , x, x^2, x^3$$} , but as I understand, it only proves linear independence and not the converse.

Show that matrix A is invertible for all values of $$ \theta$$; then find $$A^{-1}$$ using $$A^{-1}= \frac{1}{det(A)}adj(A)$$ A = cos$$ \theta$$ -sin$$ \theta$$ 0 sin$$ \theta$$ cos$$ \theta$$ 0 0 0 1 ---------- By cofactoring along the 3rd row, I find det(A) = (1)*($$...

Thank I was able to introduce a row of zeros by reducing the determinant matrices to upper triangular form thus making the determinant = 0 by taking the cofactor expansion along the row of zeros.

Yes i know if the det = 0 then the matrix is not invertible, or if i can introduce a row or columns of zeros its not invertible. im not sure but maybe there is something involved with transformations.

SHow that matrix A is not invertible, where A = $$cos^2 \alpha$$ $$sin^2 \beta$$ $$cos^2 \theta$$ a a a $$sin^2 \alpha$$ $$cos^2 \beta$$ $$sin^2 \theta$$

I can find inverses using an adjust for a 3X3 matrix. But My homework book asks us to find the inverse using an adj(A) for a 4x4 matrix. 1 3 1 1 2 5 2 2 1 3 8 9 1 3 2 2 it seems less time efficient to find the inverse using this method. Is it possible to reduce the matrix to a a simpler yet...

Let A be a square matrix, a) show that $$(I-A)^{-1}= I + A + A^2 + A^3 if A^4 = 0$$ b) show that $$(I-A)^{-1}= I + A + A^2+...+A^n $$ if $$ A^{n+1}= 0$$

My book describes a linear system with "m equations in n unknowns." Maybe this is a subtle detail but this confuses me. Shouldn't it be the other way around, "n unknowns in m equations?"

Linear equations do not have roots of variables. So why are a) and f) linear equations?

i just want to simplify this circuit so i can find the voltage across Capacitor 3. c1= 5.3 μF c2=1.2μF c3=1.3μF c4=9.4μF Vbattery=20V Is this picture I made the equivalent of the circuit above??

Thank you for the reply. At first I thought you were joking & the book made no mention. I had no idea 365.25 is the average number of days in a year.

Hi. I'm asked to convert 2 year into the SI Unit seconds: Known: 1 Hr = 3600 s 1 Day = 86400 s So using a calculator... 1 yr = 365*86,400 = 31,536,000 I want to express the answer in scientific notation: Because the lesser number on has 3 significant digits, the scientific...