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4. [10] In each of the following cases, determine (with justification) whether the given function f...
2. Determine whether or not the mapping f: R+R given by f(0) = 2 is a...
2. Determine whether or not the mapping f: R+R given by f(0) = 2 is a transformation. 3. Determine whether or not the mapping f: RR given by f(2)= is a transformation. 4. Determine whether or not the mapping f:R2 + R2 given by far,y) = (2x, 3y) is a transformation.
For each of the following, determine whether the given function can serve as the probability mass...
For each of the following, determine whether the given function can serve as the probability mass function of a random variable with the given range: a) f(x) = 2 for r = 1,2,3,4,5, b) f(x) = for x = 0, 1, 2, 3, 4, and c) f(x) = for x = 0,1,2,3,4,5.
6. Determine whether or not V spans R and choose a correct justification: 2, vs) ,...
6. Determine whether or not V spans R and choose a correct justification: 2, vs) , where vi = ,V321 (A) V spans R2 because its echelon form contains a leading entry in every column. (B) V spans R2 because r vi - b is consistent for all b e R? (C) V does not span R2, because vs is an scalar multiple of v2. (D) V does not span R2, because a set of three vectors can only span...
With justification in each one. Clarification; why if true and why if false? Please Determine whether...
With justification in each one. Clarification; why if true and why if false? Please Determine whether the following statement is true or false: • Iff: R+R is differentiable and strictly increasing on R, then f'(1) > 0 VI ER • If S: R R is continuous and f(x) - ron Q, then (V3) - 3. • If f,g: (0,1) - Rare functions such that \S(1)-f(y) = g(1)-9(y) for all 1, y € (0, 1) and g is continuous on (0,1),...
[16 marks] Provide concise answers and brief justification and reasoning (a) Determine the period of the function f(t)...
[16 marks] Provide concise answers and brief justification and reasoning (a) Determine the period of the function f(t) = n+|cos(t)(3+)sin(3tt) (b) Consider the 4-periodic function g(t) that is defined as g(t)=-(x-1)2+1 for te (0,2. Does an approximation of this function by a Fourier series converge faster for the odd or the even extension. (c) Consider the function h(t) cos2(t)+sin2 (t). Are the coefficients by of the Fourier series of this function equal to 0 for all n? (d) Consider the...
Linear Algebra Check whether the following maps are linear. Determine, in the cases that the map...
Linear Algebra
Check whether the following maps are linear. Determine, in the cases that the map is linear, the null space and the range and verify the dimension theorem 1 a. A: R2R2 defined by A(r1, r2r2, xi), b. A: R2R defined by A(z,2)2 c. A: Сз-+ C2 defined by A(21,T2, x3)-(a + iT2,0), d. A: R3-R2 defined by A(r, r2, r3) (r3l,0), C 1
Consider the following vectors 4 4 For each of the following vectors, determine whether it is...
Consider the following vectors 4 4 For each of the following vectors, determine whether it is in spana, b, c. If so, express it as a linear combination using a, b, and c as the names of the vectors above < Select an answer > 4 14 20 < Select an answer > < Select an answer >
please anyone answer all the questions as soon please 2 4 3 3 4 1. Given...
please anyone answer all the questions as soon please
2 4 3 3 4 1. Given three points A = (0,–8, 10), B = (2, -5, 11), C = (-4,-9, 7) in R3. (a) Show that these three points are not collinear (not in a straight line). (b) Find the area of the triangle ABC. (c) Find the scalar equation of the plane containing the points A, B and C. (d) Find a point D on the plane such that...
17. Given the function f(x) = ? answer the following questions: [4 Points] x+1 (a) What...
17. Given the function f(x) = ? answer the following questions: [4 Points] x+1 (a) What is the inverse function f-(x)? Show all work that leads to the final answer. (b) What is the Range of f-1(x)? 18. Determine whether the following functions represent linear data, exponential data or neither. [4 Points). f(x) х -1 g(x) 5 1 0 16 1 4 1 4 Х -1 0 1 2 3 o 2 7 1 2 3 16 Linear, Exponential or...
linear algebra 1. Determine whether the given set, along with the specified operations of addition and scalar multiplica...
linear algebra
1. Determine whether the given set, along with the specified operations of addition and scalar multiplication, is a vector space (over R). If it is not, list all of the axioms that fail to hold. a The set of all vectors in R2 of the form , with the usual vector addition and scalar multiplication b) R2 with the usual scalar multiplication but addition defined by 31+21 y1 y2 c) The set of all positive real numbers, with...
2. Determine whether or not the mapping f: R+R given by f(0) = 2 is a transformation. 3. Determine whether or not the mapping f: RR given by f(2)= is a transformation. 4. Determine whether or not the mapping f:R2 + R2 given by far,y) = (2x, 3y) is a transformation.
For each of the following, determine whether the given function can serve as the probability mass function of a random variable with the given range: a) f(x) = 2 for r = 1,2,3,4,5, b) f(x) = for x = 0, 1, 2, 3, 4, and c) f(x) = for x = 0,1,2,3,4,5.
6. Determine whether or not V spans R and choose a correct justification: 2, vs) , where vi = ,V321 (A) V spans R2 because its echelon form contains a leading entry in every column. (B) V spans R2 because r vi - b is consistent for all b e R? (C) V does not span R2, because vs is an scalar multiple of v2. (D) V does not span R2, because a set of three vectors can only span...
With justification in each one. Clarification; why if true and why if false? Please Determine whether the following statement is true or false: • Iff: R+R is differentiable and strictly increasing on R, then f'(1) > 0 VI ER • If S: R R is continuous and f(x) - ron Q, then (V3) - 3. • If f,g: (0,1) - Rare functions such that \S(1)-f(y) = g(1)-9(y) for all 1, y € (0, 1) and g is continuous on (0,1),...
[16 marks] Provide concise answers and brief justification and reasoning (a) Determine the period of the function f(t) = n+|cos(t)(3+)sin(3tt) (b) Consider the 4-periodic function g(t) that is defined as g(t)=-(x-1)2+1 for te (0,2. Does an approximation of this function by a Fourier series converge faster for the odd or the even extension. (c) Consider the function h(t) cos2(t)+sin2 (t). Are the coefficients by of the Fourier series of this function equal to 0 for all n? (d) Consider the...
Linear Algebra
Check whether the following maps are linear. Determine, in the cases that the map is linear, the null space and the range and verify the dimension theorem 1 a. A: R2R2 defined by A(r1, r2r2, xi), b. A: R2R defined by A(z,2)2 c. A: Сз-+ C2 defined by A(21,T2, x3)-(a + iT2,0), d. A: R3-R2 defined by A(r, r2, r3) (r3l,0), C 1
Consider the following vectors 4 4 For each of the following vectors, determine whether it is in spana, b, c. If so, express it as a linear combination using a, b, and c as the names of the vectors above < Select an answer > 4 14 20 < Select an answer > < Select an answer >
please anyone answer all the questions as soon please
2 4 3 3 4 1. Given three points A = (0,–8, 10), B = (2, -5, 11), C = (-4,-9, 7) in R3. (a) Show that these three points are not collinear (not in a straight line). (b) Find the area of the triangle ABC. (c) Find the scalar equation of the plane containing the points A, B and C. (d) Find a point D on the plane such that...
17. Given the function f(x) = ? answer the following questions: [4 Points] x+1 (a) What is the inverse function f-(x)? Show all work that leads to the final answer. (b) What is the Range of f-1(x)? 18. Determine whether the following functions represent linear data, exponential data or neither. [4 Points). f(x) х -1 g(x) 5 1 0 16 1 4 1 4 Х -1 0 1 2 3 o 2 7 1 2 3 16 Linear, Exponential or...
linear algebra
1. Determine whether the given set, along with the specified operations of addition and scalar multiplication, is a vector space (over R). If it is not, list all of the axioms that fail to hold. a The set of all vectors in R2 of the form , with the usual vector addition and scalar multiplication b) R2 with the usual scalar multiplication but addition defined by 31+21 y1 y2 c) The set of all positive real numbers, with...
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