Homework Answers

A square is inscribed in a circle that is inscribed in a square. Find the ratio of the areas of the two squares.

The population of a city increases at a rate proportional to the present number. It has an initial population of 50000 that increases by 15% in 10 years. What will be the population in 30

years?

Mpohlo bought nine shirts at a total cost of R2 520,00. The large shirts costs R300,00 each and the small

shirts costs R240,00 each. Choose the correct statement.

[1] He bought twice as many small shirts as large shirts

[2] He bought three large shirts

[3] He paid R720 in total for the small shirts

[4] He paid double the amount for the large shirts as the amount that he paid for the small shirts

QUESTION 3 Let A = [ 4 0 1 −2 1 0 −2 0 1 ](its 3by3 matrix).

3.1. Find the eigenvalues of A.

3.2. For each eigenvalue of A find the corresponding eigenvectors.

3.3. Is A diagonalizable? Explain. If it is diagonalizable, then find P such that 𝐷 = 𝑃 −1𝐴𝑃 is a diagonal matrix. Do not compute 𝑃 −1(show all step!) . 

When solving for x in the equation

((9x + 7)/2)-(x-(x-2))/7)=36

the equation that is NOT correct, is

[1] ((9x + 7)/2)-[(7x/7)-((x-2)/7)]=36

[2] ((9x + 7)/2)-((7x-x-2)/7)=36

[3] ((9x + 7)/2)-((6x+2)/7)=36

[4] 7(9x + 7) − 2(6x + 2) = 14 × 36.

For each of the linear operators below, determine whether it is normal, self adjoint, or neither

(a) T / (R ^ 2) -> R ^ 2 defined by T(x, y) = (2x - 2y, - 2x + 5y)

(b) T / (C ^ 2) -> C ^ 2 defined by T(x,y)=(2x+iu.x+2y)