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How do I get the eigenvalues, x, of a matrix, M, with eigenvectors, v?

To start off, let's write the equation involving these three objects: Mv = xv. Now, looking at the first form of the equation, we don't want any eigenvector to have all its entries be zero, or else the eigen...
MM
Answered by Matthew M. • Maths tutor
4587 Views

Find all the stationary points of the curve: y = (2/3)x^3 – (1/2)x^2 – 3x + 7/6 and determine their classifications.

The first thing to do is write down y’ and y’’ neatly since these are the main two equations we will be working with… y’ = 2x 2 – x – 3 & y’’ = 4x – 1… To find the stationary point we must find where y’ ...
HT
Answered by Henry T. • Maths tutor
3883 Views

How do you solve a Differential equation using integrating factors?

Check the equation is in the form dy/dx + P(x) y=Q(x) (show example) Find the int factor: I(x)=e integralP(x) dx Multiply all terms by the integrating factorMake sure you show this step clearly: d/dx(I(x)y) ...
RB
Answered by Rachael B. • Maths tutor
3730 Views

The region below the curve y = e^x + e^(-x) and the lines x = 0, x = ln4 is rotated 2π radians about the x-axis. Find the volume of the resulting solid.

We can use the formula for a Volume of Revolution: V =π ∫ (e^x + e^(-x))^2 dx, with limits x = 0, x = ln4.Expanding the brackets: (e^x + e^(-x))^2 = e^2x + 2 + e^(-2x).So: V = π ∫ (e^2x + 2 + e^(-2x)) dx = π...
RS
Answered by Rumen S. • Maths tutor
4545 Views

What is the difference between a scalar product and a vector product, and how do I know which one to use in questions?

The main thing to consider here is the output of the operation. Vector and scalar products are both operations in which you take two vectors but then get something else. In a scalar product, you get a number...
ME
Answered by Maite E. • Maths tutor
9112 Views