IITM BS Question 32 - Week 6 Practice

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IITM BS Question 32 - Week 6 Practice | Prasnya

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Q32Numerical3 Marks11 Dec 2022

Let

H

denote the matrix obtained by putting

k = 1

in the Hessian matrix (obtained in the previous comprehension). Let

T: \mathbb{R}^3 \to \mathbb{R}^3

be the linear transformation

T(x, y, z) = (v_1 x + v_1 y + v_1 z, v_2 x + v_2 y + v_2 z, v_3 x + v_3 y + v_3 z)

. If

H

is the matrix representation of

T

w.r.t. the standard ordered basis

\{v_1, v_2, v_3\}

for both domain and codomain, then find the value of

2(v_1 + v_2) + (v_2 + v_3) - (v_1 + v_3)

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Q32

00:00

11 Dec 2022

Mathematics 2 · Week 6

Q32.Let

H

denote the matrix obtained by putting

k = 1

in the Hessian matrix (obtained in the previous comprehension). Let

T: \mathbb{R}^3 \to \mathbb{R}^3

be the linear transformation

T(x, y, z) = (v_1 x + v_1 y + v_1 z, v_2 x + v_2 y + v_2 z, v_3 x + v_3 y + v_3 z)

. If

H

is the matrix representation of

T

w.r.t. the standard ordered basis

\{v_1, v_2, v_3\}

for both domain and codomain, then find the value of

2(v_1 + v_2) + (v_2 + v_3) - (v_1 + v_3)

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