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How do I calculate the eigenvalues and eigenvectors of a 2x2 matrix, and what is the point of doing this calculation?

We find the eigenvalues (here called "k") by solving the characteristic equation det(M - kI) = 0. For a 2x2 matrix ((a, b), (c,d)) the determinant is a d - b c, we set this equal to zero and solve ...
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Answered by Tutor120184 D. • Maths tutor
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Find the derivative of y=e^(2x)*(x^2-4x-2).

Notice that y can be expressed as y=f(x)g(x), in which f(x)=e^(2x) and g(x)=x^2-4x-2.Through the product rule, we know that dy/dx=f'(x)g(x)+f(x)g'(x).Through the chain rule, we can solve f(x) by rewriting in...
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Answered by Samuel H. • Maths tutor
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Solve x^2+4x-5=0

Two approaches.1.Note that the equation is a quadratic equation, and can thus be solved per the quadratic formula, in which the solutions are given to be (-b+-sqrt(b^2-4ac))/2a.Plugging in the values from th...
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Answered by Samuel H. • Maths tutor
4846 Views

Solve the equation: x^2 +8x + 12 = 0

This is a classic GCSE-style equation :) 1) Always write out the original equation for clarity (and so that you don't have to look back at the question constantly) :)x^2 + 8x + 12 = 02) Notice that this is q...
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Answered by Obaid U. • Maths tutor
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Find the derivative of y = 3x^4 - 10x^2+7x

The method used to find the derivative (dy/dx) of the equation is to: "Multiply the coefficient of x by the power then deduct the power x is raised to by 1" Step 1: 3x^4 Carry the power of 4 down a...
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Answered by Hameedat O. • Maths tutor
3974 Views