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Find the inverse of a 3x3 matrix

There are 4 key steps to this question. (i) calculate the matrix of minors: you want to find the determinant of each entry and this forms a new matrix. (ii) convert this into a matrix of cofactors: this is a...
JR
7830 Views

Find the integral of f(x)= x^3 + 2x^2 + 1

Let's work our way from left to right. Starting with the x 3 term we will take the integral with respect to x. First we add one to the power we get x 4 , next we take the coefficient and divide it by the new...
EB
3487 Views

Prove that (AB)^-1 = B^-1 A^-1

This problem can be solved in 8 steps: 1. Let AB = C 2. A -1 AB = A -1 C 3. IB = A -1 C as the identity matrix I = A -1 A 4. B -1 B = B -1 A -1 C premultiply both sides by B -1 5. I = B -1 A -1 C as B -1 B =...
KH
127821 Views

Differentiate artanh(x) with respect to x

First we set y=artanh(x). Then we rearrange such that tanh(y)=x. There several approaches to find dy/dx, but the quickest is to use implicit differentiation. The differential of tanh(y) is sech 2 y. We diffe...
SH
14260 Views

Solve x^3=1 giving all the roots between -pi<=theta<=pi in exponential form

x^3=1=e^2(pi) i k x=e^2(pi) i k/3 The three roots are k=0 x=1 k=1 x=e^2(pi)*i/3 k=-1 x=e^-2(pi) i k/3
AA
3602 Views