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MTHE 225 Quiz: quiz 6 (10).pdf

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rosereindeer362

20 Nov 2012

School

Queen's University

Department

Mathematics & Engineering Courses

Course

Professor

Gregory G Smith

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Document Summary

We are asked to use the eigenvalue method to nd a solution to the following linear system, satisfying the speci ed initial conditions. x . 2 = 6x1 2x2 , x1(0) = 1 , x2(0) = 0. 6 2! has eigenvalues = 3, = 4, as is seen from the characteristic. 5 polynomial: det(a i) = det 9 . To nd the eigenvector v corresponding to = 3, we solve the system. To nd the eigenvector v corresponding to = 4, we solve the system. Thus the two independent solutions are to nd v = 1 x1(t) = e3t 5. 1 and so the general solution is x(t) = c1e3t 5. E4t! c1 c2! x(t) = x(t)c = 5e3t c2! such that. Now we wish to nd c = c1 which can be written as. We nd c1 = 1, c2 = 6, thus or. 1! x1(t) = 5e3t + 6e4t x2(t) = 6e3t.

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1. Factor out the GCF from thepolynomial.
20m^9 + 6m^7 + 20m^5

2(10m^9 + 3m^7 +10m^5)
No common factor
m^5 (20m^4 + 6m^2 +20)
2m^5 (10m^4 + 3m^2 +10)

2. Find the solution to the system by addition(elimination) method.
4x + 15y = 15
8x - 3y = -3

(1, 0)
(0, 0)
(0, 1)
(1, 1)

3. (11p + 4)(11p - 4)

p^2 - 16
121p^2 + 88p - 16
121p^2 - 16
121p^2 - 88p -16

4. Find the solution to the system by addition(elimination) method.
2x + 15y = -91
9x + 5y = 28

(-5, 7)
(7, -7)
(9, -9)
(-7, 7)

5. Factor by grouping.
18x^3 + 15x^2 + 12x + 10

(3x^2 + 2)(6x + 5)
(18x^2 - 2)(x - 5)
(3x^2 - 2)(6x - 5)
x(18x + 2)(x +5)

6. (x + 3y)(x + 5y)

x^2 + 5xy + 15y^2
x^2 + 8xy + 8y^2
x^2 + 8xy + 15y^2
x + 8xy + 15y

7. 6x^7 (9x^7 + 12x^2 - 7)

54x^7 + 72x^2 - 42
54x^14 + 72x^9
54x^14 + 72x^9 -42x^7
54x^14 + 12x^2 -7

8. 15x^2 - 12x + 10x - 8

(15x + 2)(x - 4)
(15x - 2)(x + 4)
(3x - 2)(5x + 4)
(3x + 2)(5x -4)

9. For the polynomial, state the degree andwhether or not the polynomial is a monomial, a binomial, or atrinomial.
5x^3y^4 - 8x^5y^6 + 8

Binomial, degree 7
Trinomial, degree 3
Trinomial, degree18
Trinomial, degree11

10. (3x^8 + 2x^7 - 4x^6 + 8) + (7x^8 - 4x^7 +8x^6 + 1)

10x^8 - 2x^7 + 4x^6 +9
12x^42 + 9
10x^26 - 2x^14 + 4x^12 +9
4x^8 + 4x^7 + 4x^6 +9

11. (2n^5 - 3n^3 - 6) - (5n^5 - 14n^3 -3)

-3n^5 + 2n^3 - 9
-3n^5 + 11n^3 - 3
5n^8
-3n^5 + 11n^3 -9

12. Use the substitution method to solve thesystem.
x - 4y = -13
7x - 5y = -22

(1, 4)
(-2, 4)
(-1, 3)
No solution

13. Use the substitution method to solve thesystem.
8x - 6y = 32
2x - 2y = 8

(3, 1)
(4, 1)
(4, 0)
No solution

14. Terms in a polynomial are separated byaddition or subtraction.

15. A polynomial is an algebraic expression ofone or more terms.

16. A solution of two linear equations in twovariables is an ordered pair that is a solution to eachequation.

17. The greatest common factor will always begreater than the largest factor of each term of theexpression.

18. A system of equations in two variables mayhave infinite solutions.

19. When two or more algebraic expressions aremultiplied, each expression is called a term.

20. Factoring is multiplication inreverse.