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Further Maths: How do you find the inverse of a 2 x 2 matrix?

Consider the Matrix M: M= a b c d First, find the determinant. To do this, we use the formula: det(M) = ad - bc Then plug the information into the formula used to find the inverse: 1/det(m) x c -b -d a
SS
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Prove ∑r^3 = 1/4 n^2(n+1)^2

Proof by induction Base Case when n=1 LHS = 1^3=1 RHS= 1/4(1^2)(1+1)^2=1/4(1)(2^2)=1/4(4) Assume true for n=k so ∑r^3= 1/4k^2(k+1)^2 For n=k+1 ∑r^3 = ∑k terms + (k+1)^3 = 1/4(k^2)(k+1)^2 + (k+1)^3 = 1/4(k^2)...
JO
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How to calculate the integral of sec(x)?

First of all, multiply secx by (secx+tanx)/(secx+tanx). Use the substitution u=secx+tanx, so that du=(secxtanx+sec 2 x) dx and then substitute both terms. Calculate the integral of the du/u arriving at ln|u|...
CK
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By Differentiating from first principles, find the gradient of the curve f(x) = x^2 at the point where x = 2

This qustion can be solved easily using the gradient formular, m = ∆y/∆x, and some simple algrebra. The gradient at the point x = 2 is calculated by find the gradient of a tangent at x = 2. To find this we i...
HF
3736 Views

Find the determinant of a 3x3 square matrix

We can expand following any row or column we want. A wise choice would be to use a row/column in which we have one or more zero entries to reduce the calculations. From this, we pick the first entry on the c...
SZ
3529 Views