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Find the eigenvalues and eigenvectors of the following 3x3 matrix (reading left to right, top to bottom): (1 0 2 3 1 1 2 0 1)

The eigenvalues are given by the characteristic equation (1-x)((1-x)^2-4)=0, which gives the values x=1, x=-1 and x=3 . These eigenvalues correspond to the eigenvectors (0, 1, 0), (1, -1, -1) and (1, -5, 1) ...
JP
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The are 10 coloured balls in a bag, 4 red, 3 green, 2 orange and 1 yellow. John picks out balls and replaces them one at a time. What is the probability that the first two he picks are red?

The probability that John picks out a red ball is: The number of red balls divided by the total number of balls = 4/10 Because the balls are replaced, each event is independent so every time John picks out a...
HT
Answered by Haroon T. • Maths tutor
4587 Views

Where does the circle equation come from?

equation of a circle: (x - a)^2 + (y - b)^2 = r^2, where the circle has centre (a, b) and radius r. Let's draw the diagram, where (x, y) is some point on the circle, which for ease we'll call P, and (a, b) i...
AB
Answered by Ashwin B. • Maths tutor
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Solve the simultaneous equations. x^2 + 2y=9, y-x=3

Use the method of substitution to answer this question. Step 1: Rearrange one of the equations to find x or y. y-x=3 y=x+3 Step 2: Substitute your y into the first equation x 2 +2y=9 x 2 +2(x+3)=9 Step 3: Ex...
KW
Answered by Kieran W. • Maths tutor
5436 Views

Expand the brackets (x+1)(x-4)

When we are presented with a quadratic equation in this form, and asked to expand, it is important to make sure that every term is used. For example, we would begin with the 'x' from the (x+1) bracket, and t...
AW
Answered by Abbie W. • Maths tutor
6972 Views