A rotation matrix, corresponding to a rotation with an angle in the two-dimensional space, is defined as A = cos sin Cos - sin 1 a) Compute the determinant of A. b) Compute the inverse matrix A-¹. To which linear transformation does this correspond? Show that A is an orthogonal matrix.

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A: We use root test to check the convergence of the given series.

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Q: Problem 2 Is R^2 a subspace of R^3? Explain

A: R²={(x,y):x,y is in R} R³={(x,y,z):x,y,z is in R}

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A: bag contain total marbles = 10  pablo randomly picks =5 no of red marbles =6 no of green marbles = 3…

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A: Lean ground beef: 1 lb 4 oz Chili powder: 3 TBS Chopped Tomatoes: 1 qt Recipe makes 3 quarts chili.…

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A: I have explained everything with in the solution, please go through that

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Q: Prove that 3x + sin x + cos x = 0 mas exactly one real root.

A: The given equation is 3x+sinx+cosx=0. It can be seen that f0=1>0 and f-π=-3π-1<0.

Q: I think in the determinant J_22=1 not zero but I understand the concept. thanks

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Q: Consider the following initial value problem for y(t): (t-6) sin (9t) (t-4) (t-9) -10 y" + (y - y(6)…

A: y''+t-10t-5y'-sin9tt-4=t-6t-9y6=4y'6=-3

Q: Given a matrix A of size m by n. Prove N(A) is a subspace of R^n.

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Q: Question 7. Let A={1,2,3,..., n}. Find A' in the usual topological space on the set of real numbers.

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Q: Find the product z₁z2 and the quotient 21. Express your answers in polar form. Z2 Z1 = 4(cos(160°) +…

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Q: n>=0

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Q: 2.27 Determine the particular solution of the difference equation 5 y(n) = y(n − 1) − − y(n − 2) +…

A: Here the differential equation is given by  y(n) = 5/6y(n - 1) - 1/6y(n - 2) + x(n). The forcing…

Q: 4. Find the number of integer solutions for the following equality using inclusion-exclusion method:…

A: We shall use counting using coefficients

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Q: Let F = (6x²y + 2y³ + 8eª)i + (6eª² +54x) j. Consider the line integral of around the circle of…

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