Question

Let (x1, x2, x3 and (y1, y2, y3 represent the coordinates with respect to the bases

B1 = {(1, 0, 0), (0, 1, 0), (0, 0, 1)}, B2 = {(1, 0, 0), (0, 1, 2), (0, 2, 1)}. If

Q(X ) = x12 + 2x1x2 + 2x2x3 + x22 + x32, find the representation of Q in terms of

(y1, y2, y3).

02 Feb 2018
Answer :
Word Count : 597
To solve this problem, we need to transform the coordinates of the function \( Q(X) \) in terms of the new coordinate system defined by the basis \( B_2 \) from the original basis \( B_1 \). We are given the function \( Q(X) \) in terms of the coordinates \( (x_1, x_2, x_3) \) in the basis \( B_1 \): \[ Q(X) = x_1^2 + 2x_1x_2 + 2x_2x_3 + x_1^2 + x_3^2 \] And we need to express this in terms of \( (y_1, y_2, y_3) \), which are the coordinates in the basis \( B_2 \). ### Step 1: Express \( B_2 \) in terms of \( B_1 \) We first need to express the change of basis matrix from \( B_1 \) to \( B_2 \). The two bases are: - \( B_1 = \{ (1, 0, 0), (0, 1,
_____ ______ ____ _________ _____ ______.
_____ _______ ______ _________ ____ _____.
_________ _______ __________ _______ _______.
__________ ________ ___ ______ __________ _________.
___ ________ __________ _______ ________ ____.
_______ ___ ___ _______ ________ _____ __________ _______.
__________ _____ ____ ____ __________ _____ __________ __________ ________ _____.
___ _____ _________ ___ _________.
_______ ______ ______ _________ _________ _________ ______ _______ ______.
_____ ________ _______ __________ ___ _____ ________ _____.
____ _____ _________ ______ _________ ______.
_______ ____ ________ _________ __________ ____ ________ __________ _________ ______ _________ ________.
____ ____ ____ ______ ____ _____ ___.
_____ ___ ___ _____ ______.
_______ _______ _______ ________ _________ _________ ______.
_____ _______ ______ ________ ____ _________ ________.
_____ _______ _____ _______ ______ ______ ___ ______ __________ _____ __________ ___.
____ _______ _____ _________ ________ _________ _______ ___.
________ ___ ___ ____ _____ ____.
_______ __________ _______ ________ __________ ______ _______ _________ _____ ____.
_________ ___ _____ __________ ________ _____ ________ ________ _________ _______ _____.
_______ ______ _____ _______ _______ ___.
____ _________ _________ _______ ___ ___.
__________ _____ _________ ________ ________ _____ ________ ___ ___ __________.
________ ____ _______ ___ __________ ________ _____ ______.
_____ ______ ____ ______ ___.
_______ ____ _________ ____ ______ _________.
_________ ________ ____ _______ _____ _____ ___ _________ _______.
___ ________ ___ ______ _______ ________ __________.
________ ____ _______ _______ _________ ________.
________ __________ __________ ______ ___ ______ __________ _________ _______ _________.
_____ _____ ________ ____ ________ ________ ______ __________ _______ _____ ______ _______.
________ ____ _________ ________ _________ ___ __________ _______ __________ ________ _________ _____.
______ _______ _________ ____ _________ _____ _____.
____ __________ ______ ________ __________ ___ _________ _____ __________ __________ _________ _______.
____ ________ _______ ____ ________ ___ _____ _____ ____.
________ ____ __________ ____ _____ ______ ___ ___ _________ ______ ____ _______.
______ __________ __________ _________ ___ _______ ______ _____.
____ ___ ___ _____ ______ __________.
_____ ___ _______ __________ _______ _______ __________ ________.
__________ ________ ____ __________ __________ __________ ________ _______ ___ ___.
______ _____ ______ _____ ___ _______ __________ ________ ______ __________ ______.
__________ ____ ___ ____ _____ _________ _________ _______ _____.
________ _____ _______ __________ ________ ________ ____ ___.
_____ ____ _________ _____ ______ _______ ____.
______ __________ _____ ________ ___ __________ _____.
___ ____ _______ ____ ______ ______.
________ __________ __________ ___ _________ _____ ____.
_____ ____ _______ ________ _____ ___ ______ ____ _____.
________ _______ _____ ________ ________ _______ ____ ________ __________.
______ __________ ______ ____ _______ _______ _________ _____ ____ __________ ______ ________.
_______ __________ ______ ___ ___ ________ ____ _____ _____ __________.
_____ ____ ______ __________ _____ __________ ______ ________.
_________ ________ ___ ____ _____ ___ ___ _______ _____.
__________ _____ _______ _____ __________ ______ _________ ___.
______ ______ __________ __________ ______.
IGNOU ACADEMY
Your IGNOU journey, made easier.
  • Solved Assignments
  • Study Notes
  • Guess Papers
  • Question Papers
Call Us WhatsApp
STUDY • PREPARE • SUCCEED
Skip in 10
Related Questions

Check whether the following system of equations has a solution. 

4x + 2y + 8z + 6w = 3

2x + 2y + 2z + 2w = 1

x + 3z + 2w = 3

 

Let T : P2 → P1 be defined by

T (a + bx + cx2) = b + 2c + (a − b)x.

 Check that T is a linear transformation. Find the matrix of the transformation with respect to the ordered bases B1 = {x2, x2 + x, x2 + x + 1} and B2 = {1, x}. Find the kernel of T. .

Complete the set S = {x3+x2+1,x2+x+1,x+1} to get a basis of P3

Check whether the vector  (2,sqrt(3),3) sis equally inclined to the vectors (2,2 sqrt(3)) and (4,0).

Find inverse of the matrix B in part a) of the question by finding the adjoint as well as using Cayley-Hamiltion theorem.

Define T : R3 → R3 by

T (x, y, x) = (x + y, y, 2x − 2y + 2z).

Check that T satisfies the polynomial (x − 1)2(x − 2). Find the minimal polynomial of T .

Check whether the matrices A and B are diagonalisable. Diagonalise those matrices which are diagonalisable.

Image ignouacademy-com--p-2018-22444

Image ignouacademy-com--p-coordinates-19165

 

 

IGNOU Solved Assignments Assignments Ignou Projects Project Previous Year Solved Exam Papers Notes Notes Sample Question Papers Sample Question Papers
Login
Top
📞
Call Support Instant phone assistance IGNOU MTE 2 2018 - Let (x1, x2, x3 and (y1, y2, y3 represent the coordinates with respect | IGNOU Academy
→
🟢
WhatsApp Chat Fast live messaging
→
Email Us Business enquiries & support
→