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Let V be the vector space of polynomial functions of degree three or less. Let the ordered basis for V consisting of the functions of the four functions xj : j = 0, 1, 2, 3 and let D be the differentiation operator. Then the matrix of D in the above ordered basis is
- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
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Let V be the vector space of polynomial functions of degree three or l...
Let V be the vector space of polynomial functions of degree three or less. Let the ordered basis for V consisting of the functions
xj : j = 0 ,1 ,2 , 3
and let D be the differentiation operator. We need to find the matrix of differentiation operator D in the basis xj, j = 0,1, 2, 3, that is {1, x, x2, x3}.
Therefore, D(1) = d/dx(1) = 0
= 0.1 + 0.x + 0.x2 + 0.x3
D(x) = d/dx (x) = 1 = 1.1 + 0 . x + 0 .x2 + 0.x3 ax
D(x2) =d/dx(x2) = 2x = 0.1 + 2.x + 0.x2 + 0.x3 ax
D(x3) = d/dx (x3) = 3x2 = 0.1 + 0.x + 3.x2 + 0.x4
Thus, the matrix of differentiation operator
is
xj : j = 0 ,1 ,2 , 3
and let D be the differentiation operator. We need to find the matrix of differentiation operator D in the basis xj, j = 0,1, 2, 3, that is {1, x, x2, x3}.
Therefore, D(1) = d/dx(1) = 0
= 0.1 + 0.x + 0.x2 + 0.x3
D(x) = d/dx (x) = 1 = 1.1 + 0 . x + 0 .x2 + 0.x3 ax
D(x2) =d/dx(x2) = 2x = 0.1 + 2.x + 0.x2 + 0.x3 ax
D(x3) = d/dx (x3) = 3x2 = 0.1 + 0.x + 3.x2 + 0.x4
Thus, the matrix of differentiation operator
isMost Upvoted Answer
Let V be the vector space of polynomial functions of degree three or l...
Let V be the vector space of polynomial functions of degree three or less. Let the ordered basis for V consisting of the functions
xj : j = 0 ,1 ,2 , 3
and let D be the differentiation operator. We need to find the matrix of differentiation operator D in the basis xj, j = 0,1, 2, 3, that is {1, x, x2, x3}.
Therefore, D(1) = d/dx(1) = 0
= 0.1 + 0.x + 0.x2 + 0.x3
D(x) = d/dx (x) = 1 = 1.1 + 0 . x + 0 .x2 + 0.x3 ax
D(x2) =d/dx(x2) = 2x = 0.1 + 2.x + 0.x2 + 0.x3 ax
D(x3) = d/dx (x3) = 3x2 = 0.1 + 0.x + 3.x2 + 0.x4
Thus, the matrix of differentiation operator is
xj : j = 0 ,1 ,2 , 3
and let D be the differentiation operator. We need to find the matrix of differentiation operator D in the basis xj, j = 0,1, 2, 3, that is {1, x, x2, x3}.
Therefore, D(1) = d/dx(1) = 0
= 0.1 + 0.x + 0.x2 + 0.x3
D(x) = d/dx (x) = 1 = 1.1 + 0 . x + 0 .x2 + 0.x3 ax
D(x2) =d/dx(x2) = 2x = 0.1 + 2.x + 0.x2 + 0.x3 ax
D(x3) = d/dx (x3) = 3x2 = 0.1 + 0.x + 3.x2 + 0.x4
Thus, the matrix of differentiation operator
is
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Let V be the vector space of polynomial functions of degree three or less. Let the ordered basis for V consisting of the functions of the four functions xj: j = 0, 1, 2, 3 and let D be the differentiation operator. Then the matrix of D in the above ordered basis isa)b)c)d)Correct answer is option 'A'. Can you explain this answer?
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Let V be the vector space of polynomial functions of degree three or less. Let the ordered basis for V consisting of the functions of the four functions xj: j = 0, 1, 2, 3 and let D be the differentiation operator. Then the matrix of D in the above ordered basis isa)b)c)d)Correct answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let V be the vector space of polynomial functions of degree three or less. Let the ordered basis for V consisting of the functions of the four functions xj: j = 0, 1, 2, 3 and let D be the differentiation operator. Then the matrix of D in the above ordered basis isa)b)c)d)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let V be the vector space of polynomial functions of degree three or less. Let the ordered basis for V consisting of the functions of the four functions xj: j = 0, 1, 2, 3 and let D be the differentiation operator. Then the matrix of D in the above ordered basis isa)b)c)d)Correct answer is option 'A'. Can you explain this answer?.
Let V be the vector space of polynomial functions of degree three or less. Let the ordered basis for V consisting of the functions of the four functions xj: j = 0, 1, 2, 3 and let D be the differentiation operator. Then the matrix of D in the above ordered basis isa)b)c)d)Correct answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let V be the vector space of polynomial functions of degree three or less. Let the ordered basis for V consisting of the functions of the four functions xj: j = 0, 1, 2, 3 and let D be the differentiation operator. Then the matrix of D in the above ordered basis isa)b)c)d)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let V be the vector space of polynomial functions of degree three or less. Let the ordered basis for V consisting of the functions of the four functions xj: j = 0, 1, 2, 3 and let D be the differentiation operator. Then the matrix of D in the above ordered basis isa)b)c)d)Correct answer is option 'A'. Can you explain this answer?.
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Let V be the vector space of polynomial functions of degree three or less. Let the ordered basis for V consisting of the functions of the four functions xj: j = 0, 1, 2, 3 and let D be the differentiation operator. Then the matrix of D in the above ordered basis isa)b)c)d)Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Let V be the vector space of polynomial functions of degree three or less. Let the ordered basis for V consisting of the functions of the four functions xj: j = 0, 1, 2, 3 and let D be the differentiation operator. Then the matrix of D in the above ordered basis isa)b)c)d)Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Let V be the vector space of polynomial functions of degree three or less. Let the ordered basis for V consisting of the functions of the four functions xj: j = 0, 1, 2, 3 and let D be the differentiation operator. Then the matrix of D in the above ordered basis isa)b)c)d)Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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