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The real symmetric matrix C corresponding to the quadratic form Q = 4x1X2 - 5x2X2 is
? Related: Linear Algebra (Part - 2)
Most Upvoted Answer
The real symmetric matrix C corresponding to the quadratic form Q = 4x...
Solution:
Given quadratic form Q = 4x1X2 - 5x2X2, we need to find the real symmetric matrix C corresponding to it.
Real symmetric matrix:
A real symmetric matrix is a square matrix that is equal to its transpose. It means that the element in the ith row and jth column is equal to the element in the jth row and ith column.
Steps to find the real symmetric matrix:
1. First, we need to write the quadratic form Q in the matrix form.
Q = [x1, x2] [0 2; 2 -5] [x1; x2] = xTCx
Here, C is the real symmetric matrix that we need to find.
2. Now, we need to find the matrix C by comparing the coefficients of x1^2, x2^2, and x1x2 in the quadratic form.
Q = 4x1X2 - 5x2X2
Comparing with xTCx, we get:
C = [0 2; 2 -5]
Therefore, the real symmetric matrix C corresponding to the quadratic form Q = 4x1X2 - 5x2X2 is [0 2; 2 -5].
Given quadratic form Q = 4x1X2 - 5x2X2, we need to find the real symmetric matrix C corresponding to it.
Real symmetric matrix:
A real symmetric matrix is a square matrix that is equal to its transpose. It means that the element in the ith row and jth column is equal to the element in the jth row and ith column.
Steps to find the real symmetric matrix:
1. First, we need to write the quadratic form Q in the matrix form.
Q = [x1, x2] [0 2; 2 -5] [x1; x2] = xTCx
Here, C is the real symmetric matrix that we need to find.
2. Now, we need to find the matrix C by comparing the coefficients of x1^2, x2^2, and x1x2 in the quadratic form.
Q = 4x1X2 - 5x2X2
Comparing with xTCx, we get:
C = [0 2; 2 -5]
Therefore, the real symmetric matrix C corresponding to the quadratic form Q = 4x1X2 - 5x2X2 is [0 2; 2 -5].
Community Answer
The real symmetric matrix C corresponding to the quadratic form Q = 4x...
The correct option is D[0 2 2 −5]
The given quadratic form is in 2-variables x1andx2.
So we can represent it as
Q = 0.x1.x1 + 2.x1.x2 + 2.x2.x1 − 5.x2.x2
So corresponding matrix C can be represented as
C = [0 2 2 −5] ∼[a11 a12 a21 a22]
The given quadratic form is in 2-variables x1andx2.
So we can represent it as
Q = 0.x1.x1 + 2.x1.x2 + 2.x2.x1 − 5.x2.x2
So corresponding matrix C can be represented as
C = [0 2 2 −5] ∼[a11 a12 a21 a22]
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The real symmetric matrix C corresponding to the quadratic form Q = 4x1X2 - 5x2X2 is Related: Linear Algebra (Part - 2)?
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The real symmetric matrix C corresponding to the quadratic form Q = 4x1X2 - 5x2X2 is Related: Linear Algebra (Part - 2)? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The real symmetric matrix C corresponding to the quadratic form Q = 4x1X2 - 5x2X2 is Related: Linear Algebra (Part - 2)? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The real symmetric matrix C corresponding to the quadratic form Q = 4x1X2 - 5x2X2 is Related: Linear Algebra (Part - 2)?.
The real symmetric matrix C corresponding to the quadratic form Q = 4x1X2 - 5x2X2 is Related: Linear Algebra (Part - 2)? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The real symmetric matrix C corresponding to the quadratic form Q = 4x1X2 - 5x2X2 is Related: Linear Algebra (Part - 2)? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The real symmetric matrix C corresponding to the quadratic form Q = 4x1X2 - 5x2X2 is Related: Linear Algebra (Part - 2)?.
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