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?"
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??
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...