Question

Reduce the quadratic form 2x^2 + 2y^2 + 2x^2 - 2yx - 2xy to the canonical form by orthogonal reduction. Hence find nature, rank, index, and signature.

          Reduce the quadratic form 2x^2 + 2y^2 + 2x^2 - 2yx - 2xy to the canonical form by orthogonal reduction. Hence find nature, rank, index, and signature.
        

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Elementary and Intermediate Algebra
Elementary and Intermediate Algebra
Alan S. Tussy, R. David Gustafson 5th Edition
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Reduce the quadratic form 2x^2 + 2y^2 + 2x^2 - 2yx - 2xy to the canonical form by orthogonal reduction. Hence find nature, rank, index, and signature.
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Transcript

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00:01 In this question, we have been given a differential equation.
00:04 We need to use an inhalator method to find a differential operator that will annihilate the non -homogeneity of e -res to 2x minus x squared.
00:14 Okay, so we know that what is the definition of annihilator.
00:18 Okay, so first of all, let us see the first part.
00:21 Okay, so let me write down what is annihilator.
00:26 Okay.
00:27 So annihilator, let's say it is q.
00:30 Okay.
00:31 Let's say my annihilator is q.
00:35 Okay, so that means what? q of f of x is zero for every x belonging to ab.
00:46 Okay, for every x belonging to the interval ab.
00:52 Okay.
00:54 And we have been given here.
00:56 We have to remove the non -overgenity of e -rays to 2x minus.
01:02 Minus x squared, okay? so e raised to 2x minus x squared...
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