Find the coordinate matrix of x relative to the orthonormal basis B in R". x = (10, 20, 5), B = {()(-), (o. o, 1)} [x]g = | 1

Q: Let A be an invertible matrix. Show that det (adj (A)) = det (A-¹).

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Q: 4. Define Let T: M2x2 (R) → P2(R) by T (a b) = (a + b) + (2d) x + ba². c d B = {69). C )·(9)· (9)}…

A: We will find the matrix with respect to the basis.

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Q: . Prove that the matrix A = Cos 0 sin 0 - sin 0 cos - has no real eigenvalues for 0 < 0 < T.

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Q: 3) Let S contain vectors of the form f(x) = a + bx + cx² + dx³ : f(-2) = 0 and f'(-4)= 0: Then a…

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A: Given matrix is A = -5-2005-1-2-30

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A: Dear student, as per our guidelines we can answer only first three subqustions. So kindly resubmit…