Let be defined by T(p(x)) = pandquot;(x) + p(x). Then the matrix representation of T with respect to basis {1, x, x2, x3} and {1, x, x2} ofand respectively isa)b)c)d)Correct answer is option 'B'. Can you explain this answer?

Explore Courses Mathemat... Exam Mathemat... Test Series Free Notes EduRev Infinity

Open App

Mathematics Exam > Mathematics Questions > Let be defined by T(p(x)) = p"(x) + p(x...

Let

be defined by T(p(x)) = p"(x) + p'(x). Then the matrix representation of T with respect to basis {1, x, x², x³} and {1, x, x²} of

and

respectively is

Correct answer is option 'B'. Can you explain this answer?

Join for Free

Join for Free

Most Upvoted Answer

Let be defined by T(p(x)) = p"(x) + p(x). Then the matrix repres...

Community Answer

Let be defined by T(p(x)) = p"(x) + p(x). Then the matrix repres...

We are given a linear transformation T: P₃[0,1] → P₂[0,1] defined by T(p(x)) = p''(x) + p'(x).

To find the matrix representation of T with respect to the bases {1, x, x², x³} for P₃[0,1] and {1, x, x²} for P₂[0,1], we apply T to each basis element of P₃[0,1].

For 1, T(1) = 0 + 0 = 0.

For x, T(x) = 0 + 1 = 1.

For x², T(x²) = 2 + 2x = 2 + 2x.

For x³, T(x³) = 6x + 3x² = 6x + 3x².

Express these results in the basis {1, x, x²}:
- T(1) = 0 → (0, 0, 0)
- T(x) = 1 → (1, 0, 0)
- T(x²) = 2 + 2x → (2, 2, 0)
- T(x³) = 6x + 3x² → (0, 6, 3)

These vectors form the columns of the matrix representation:
- Matrix:
  - 0 1 2 0
  - 0 0 2 6
  - 0 0 0 3

The correct answer is B.

Answer this doubt

Explore Courses for Mathematics exam

Similar Mathematics Doubts

Let T : P3[0 ,1] --> P2[0 , 1] be defined by (Tp) (x) = P"(x) + P(x). Then the matrix representation of T with respect to the basis {1, x, x2, x3} and {1, x, x2} of P3[0, 1] and P2[0, 1], respectively is

View answer

Let be the vector space (over R) of all polynomials of degree 3with real coefficients. Consider the linear transformation T: P P defined byThen the matrix representation M ofT with respect to the ordered basis {1, x, x2, x2 }satisfies

View answer

Let be defined by T(x, y, z) = (x + y + z, -x - y, -x - z) and M be its matrix with respect to standard ordered basis. The matrix M is similar to a matrixwhich is

View answer

be the linear transformation given by T(x,y, z) = (x,y) with respect to standard basis ofand the basis {(0,1). (1,1)} ofWhat is the matrix representation of T?

View answer

Consider the linear transformation T : R7----> R7 defined by T (x1, x2,., x6, x7) = (x7, x6,.,x2,x1) Q. Which of the following statements is true.

View answer

Question Description
Let be defined by T(p(x)) = p"(x) + p(x). Then the matrix representation of T with respect to basis {1, x, x2, x3} and {1, x, x2} ofand respectively isa)b)c)d)Correct answer is option 'B'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let be defined by T(p(x)) = p"(x) + p(x). Then the matrix representation of T with respect to basis {1, x, x2, x3} and {1, x, x2} ofand respectively isa)b)c)d)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let be defined by T(p(x)) = p"(x) + p(x). Then the matrix representation of T with respect to basis {1, x, x2, x3} and {1, x, x2} ofand respectively isa)b)c)d)Correct answer is option 'B'. Can you explain this answer?.

Solutions for Let be defined by T(p(x)) = p"(x) + p(x). Then the matrix representation of T with respect to basis {1, x, x2, x3} and {1, x, x2} ofand respectively isa)b)c)d)Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics. Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.

Here you can find the meaning of Let be defined by T(p(x)) = p"(x) + p(x). Then the matrix representation of T with respect to basis {1, x, x2, x3} and {1, x, x2} ofand respectively isa)b)c)d)Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Let be defined by T(p(x)) = p"(x) + p(x). Then the matrix representation of T with respect to basis {1, x, x2, x3} and {1, x, x2} ofand respectively isa)b)c)d)Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Let be defined by T(p(x)) = p"(x) + p(x). Then the matrix representation of T with respect to basis {1, x, x2, x3} and {1, x, x2} ofand respectively isa)b)c)d)Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Let be defined by T(p(x)) = p"(x) + p(x). Then the matrix representation of T with respect to basis {1, x, x2, x3} and {1, x, x2} ofand respectively isa)b)c)d)Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Let be defined by T(p(x)) = p"(x) + p(x). Then the matrix representation of T with respect to basis {1, x, x2, x3} and {1, x, x2} ofand respectively isa)b)c)d)Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Mathematics tests.