MATH 2211 Quiz: Quiz6mt210Sample1Ans

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turquoisegnu128

31 Jan 2019

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Find the standard matrix of s t. Note that the domain of t is r2 and the codomain is r3. We need to consider the 2 2 identity matrix. T(e1) = (1, 0, 1), t(e2) = (1, 1, 1) or. Therefore, the standard matrix a of t is given as. T(x) = a x where a = . Note that the domain of s is r3 and the codomain is r3. We need to consider the 3 3 identity matrix. S(e1) = (1, 1, 1), s(e2) = (1, 1, 1), s(e3) = (1, 1, 1), or. Therefore, the standard matrix b of s is given as. S(x) = b x where b = . We get the standard matrix of s t as.

Related Questions

K(x,y,z) = (x, x + y,x + y + z)

L(x,y,z) = (2x - y, x + 2y)

S(x,y,z) = (z,y,x)

T(x,y) = (2x + y,x + y,x - y,x - 2y)

G: R^3 -> M(2,2) defined by G(x,y,z) = (y z , (-x + y) -x)

H: M(2,2) -> P2 defined by H(a b, c d) = (a + b) + (a - 2d)x+ dx^2

Find the indicated linear transformation if it is defined. ifnot defined explain why it is not:

1) K + S

2) GS

3)2S^3 - S^2 + 3S - 4I

Find the matrix that represent each of the linear transformationK,L,S,and T for the following

1)TL

2)K + S

Find the matrix that represent each of linear transformation intwo ways, first using the result normal way and using therepresention of the matrix.

T:R^3 --> R^4 given by T(X) = Ax, where

A = [1 1 0

2 0 3

-1 1 1

1 1 2]

and v1 = (-3,3,2) v2 = (0,0,0)

2) T: R^4 --> R given by T(x1,x2,x3,x4) = x1 + 2x2 + 3x3 +4x4 and v1 = (1,2,1,-2) v2 = (2,3,0,-2)

3)T: M(2,3) --> P2

P2 = (a11 + a13)x^2 + (a21 - a22)x + a23

v1 = [-1 3 1

2 2 0]

v2 = [2 1 -2

1 1 0]

& determine wheter w1 or w2 is the iamge of thecorresponding linear transformation

w1 = x^2 + 2x + 1,w2 = x - 2.

I need help with these as soon as possible Please. Thank You!!

Q15. In 1990, the population of a country was estimated at 4 million. For any subsequent year the population, P(t) (in millions), can be modeled by the equation P(t) = 240/(5 + 54.99e^-0.0208t), where t is the number of years since 1990. Estimate the year when the population will be 21 million.
a. approximately the year 2093
b. approximately the year 2041
c. approximately the year 2088
d. approximately the year 2016

Q18. A size 6 dress in Country C is size 52 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = 2(x + 20). Find a formula for the inverse of the function described.
a. f ^-1(x) = (x - 20)/2
b. f ^-1(x) = x - 20
c. f ^-1(x) = (x/2) - 20
d. f ^-1(x) = (x/2) + 20

Q19. If f(x) = 4^x and g(x) = 12, find the point of intersection of the graphs of f and g by solving f(x) = g(x). Give an exact answer.
a. (log ₄ 12, 12)
b. (log ₄ 12, 4)
c. (log ₄ 12, 0)
d. (12, 12)

Q20. Find functions f and g so that f â g = H(x) = (5 - 2x³)².
a. f(x) = 5 - 2x³ ; g(x) = x²
b. f(x) = (5 - 2x)³ ; g(x) = x²
c. f(x) = x² ; g(x) = 5 - 2x³
d. f(x) = x³ ; g(x) = (5 - 2x)²

Q29. Solve the system of equations using Cramer's Rule if it is applicable.

a. x = 9, y = 2, z = 5; (9, 2, 5)
b. x = 8, y = 4, z = 5; (8, 4, 5)
c. x = 4, y = 5, z = 4; (4, 5, 4)
d. x = 8, y = -4, z = -5; (8, -4, -5)

Q30. Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.

a. x = 2, y = 3, z = -7; (2, 3, -7)
b. x = 1, y = 3, z = -4; (1, 3, -4)
c. x = 5, y = 13/2, z = -3; (5, 13/2, -3)
d. x = 1, y = -3, z = -16; (1, -3, -16)

Q33. Write the partial fraction decomposition of the rational expression (4x³ + 4x²)/(x² + 5)².
a. (4x - 4)/(x² + 5) + (-20x + 20)/(x² + 5)²
b. (4x + 4)/(x² + 5) + (-20x - 20)/(x² + 5)²
c. (4x + 4)/(x² + 5) + (20x - 20)/(x² + 5)²
d. (4x + 4)/(x² + 5) + (20x + 20)/(x² + 5)²

Q34. Solve the linear programming problem. Minimize z = 11x + 6y + 7 subject to: x = 0, y = 0, x + y = 1.
a. minimum: 7
b. minimum: 18
c. minimum: 24
d. minimum: 13

Q35. Solve the system of equations by elimination.

a. x = 10, y = 0; (10, 0)
b. x = 10, y = 10; (10, 10)
c. x = 0, y = 10; (0, 10)
d. x = 0, y = 0; (0, 0)

Q36. Perform the row operations on the given augmented matrix.

a.
b.
c.
d.

Q37. Solve the system of equations using Cramer's Rule if it is applicable.

a. x = -4, y = 3; (-4, 3)
b. x = -3, y = -4; (-3, -4)
c. x = 4, y = 3; (4, 3)
d. x = 3, y = 4; (3, 4)

Q38. Write the partial fraction decomposition of the rational expression x/(x² - 9x + 20).
a. -4/(x - 4) + 5/(x - 5)
b. -5/(x - 4) + 4/(x - 5)
c. 4/(x - 4) + -5/(x - 5)
d. -4/(x - 4) + -5/(x - 5)

Q39. Solve the system of equations.

a. x = -4, y = 4, z = -3; (-4, 4, -3)
b. x = -3, y = 4, z = -4; (-3, 4, -4)
c. x = -4, y = -3, z = 4; (-4, -3, 4)
d. inconsistent

Q40. Find the value of the determinant.

a. 224
b. 24
c. -72
d. 72