Example 2 Let A = [aij], B = [bj] be two nx n matrices in Mnxn with inner product (A, B) = tr (ATB) a11b11 + a22b22 + Show that the matrices A [02] are orthogonal = + annbnn. B [18], 11 =

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Q: Q4: Answer two only: (A): If A = 2 2 3 11 NET-AN 1 0; B = 2 -2 -2 and C = 0 2 -1 2 1 4 2 0 -2 -1 11…

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Q: (B): If A = 2t + 3j-4k; B=3i-4j+5k and C=i+j-k, find: (1)Ã.B (u)B.C (U)Ã. (B+C)and (A + B). (iv)…

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Q: (B): Find the unit vector perpendicular to the vectors: 3i - 4j+5k 4i + 5j-6k (PUBIEN

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Q: Q5: Find for the following functions: (4) y = x sinh 2x-cosh 2x (2) y = tan³√cot(7x) ; (3) y = sin²…

A: Sol:- (2) ddxtan3cot7x Apply the chain rule =3tancot7x2ddxtancot7x

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A: here we can use that the volume integral over vector form is simply integral in different direction.

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Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: (1) limx-ol-cos x 2 sin²x (2) limx-0 x-³…

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Q: writ the following numbers in order from least to greatest: 56/6,8 7/8,42/5,8.2,-8 3/5

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Q: 3.5 m 25 N 1.5 1 0.5 0 -0.5 -1.5 -2 -2.5 -3 -3.5 -4 45 5 个 个 千 11 ↑ ↑ ↑ ↑ ↑ 1 1 11 1 7 V 1 11 11 A >…

A: given direction field we have to find corresponding differential equation.

Q: 5. Use spectral decomposition to orthogonally diagonalize the matrix A = 5 10 {]. 5

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Q: Use row reduction to solve the following system. = 3 X1 - 4x₂ + 2x3 3x2 + 5x3 = -7 -2x₁ + 8x₂ - 4x3…

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Q: 5. Show that M:= {ECR: E is countable or E is countable} is a o-algebra.

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Q: Use the Laplace transform to solve the initial-value problem y' + 3y = 13 sin2t, y(0) = 6

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Q: I. Modified TRUE or FALSE. Write Tolits if statement is true and Tol if statement is fals statement,…

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