Math Answers

Find the orthogonal canonical reduction of the quadratic form
−x2+y2+z2+ 2xy− 2xz+ 2yz. Also, find its principal axes

Find the orthogonal canonical reduction of the quadratic form
−x2+y2+z2+ 2xy− 2xz+ 2yz. Also, find its principal axes

Which of the following statements are true and which are false? Justify your answer with a
short proof or a counterexample.
i) The relation ∼ defined by R by x ∼ y if x ≥ y is an equivalence relation.
ii) If S1 and S2 are finite non-empty subsets of a vector space V such that [S1] = [S2],
then S1 and S2 have the same number of elements.
iii) For any square matrix A, ρ(A) = det(A)
iv) The determinant of any unitary matrix is 1.
v) If the characteristic polynomials of two matrices are equal, their minimal
polynomials are also equal.
vi) If the determinant of a matrix is 0, the matrix is not diagonalisable.
vii) Any set of mutually orthogonal vectors is linearly independent.
viii) Any two real quadratic forms of the same rank are equivalent over R.
ix) There is no system of linear equations over R that has exactly two solutions.
x) If a square matrix A satisfies the equation A2 = A, then 0 and 1 are the eigenvalues of
A.

In a University, 20% of all students are graduates and 80% are undergraduates.
The probability that a graduate student is married is 0.5 and the probability that an
undergraduate student is married is 0.1. One student is selected at random. What
is the probability that (i) he/she is married (ii) the student is a graduate if he/she is
found to be married?

Mariana and reena go to local ice cream shop. Ice cream sundaes cost 2$ and banana splits cost 3$. They buy 6 more banana split than sundaes and spent a total of 28$. Define variables and write system of equation representing the information.

Assuming that it is true that 2 in 10 industrial accidents are due to fatigue, find the
probability that exactly 2 of 8 industrial accidents will be due to fatigue.

In (triangle) ABC, <C is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth. Show your work.

Find the values of the 30th and 90th percentiles of the data. Please show your work.
129, 113, 200, 100, 105, 132, 100, 176, 146, 152

Verify the identity. Justify each step.
sec 0 sec 0
__________ - __________=2 csc 0
csc 0-cot 0 csc 0+cot 0

A car rental company charges a one-time application fee of 25 dollars, 45 dollars per day, and 12 cents per mile for its cars.

How do I find the recursive definition for an arithmetic sequence

for each of the following curves, make a sketch of the curve and find:
I. the gradient function
II. the gradient of the tangent at the given point.
a. y=X2 + 3 at point (2,7)
b. y=y2 + k at point (1,1 + k)