1.3.2 Determine which of the following functions are and are not linear forms. *(a) The function f : R" → R defined by f(v) = ||v||. (b) The function f : F" → F defined by f(v) =v1. *(c) The function f: M2 → M2 defined by %3D | a b. a d (d) The determinant of a matrix (i.e., the function det : Mn → F). ẩjThe funcẩiẩnẩẩj: P → R defined by g(f) = f'(3), where f' is the derivative of f. (f) The function g :C → R defined by g(f) = cos(f(0)).

Q: 3. 6. 7 # 4. Let A 2 3 What is det(A), the determinant of A? 4 (A)0 (B) – 5 (C) 5 (D) – 24 (E) 24

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Q: What is the determinant of the 7 x 7 matrix whose (i, j)-th entry is i/?

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Q: "he determinant of the matrix 1 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 A = |1 2 3 4 5 6 7…

A: Here since the columns of matrix A is linearly dependent

Q: sin x COS X [ COS X - sin x

A: Answer and explanation is given below..

Q: Let X and Y denote be as follows: E(X) = 10, E(X2) = 125, E(Y) = 20, Var(Y) =100 , and Var(X+Y) =…

A: Given data E(X) = 10, E(X2) = 125, E(Y) = 20, Var(Y) =100 , and Var(X+Y) = 155.  W = 2X-Y and  T =…

Q: 3.2.1 Example A Consider the three functions f1(k) = 3*, f2(k) = 3k+2, f3(k) = 2*, (3.39) and form…

A: We have to solve given problem:

Q: Consider the matrix 1 4 A = 2 3 (a) Compute A-1 (b) Find det(A-') (c) Deduce a relation (if it…

A: Given the matrix A = 1423 a) compute A-1 A-1=1Aadj A adj A = 3-4-21 A = 3-8 = -5…

Q: 15) Using the properties of determinants or otherwise, show that 1 a² + a²³ 1 a+a²³=0. 1 a a² a³…

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Q: (5) 4. Are the matrices 2 (13). (3) (43) 4 5 If Not, find dependence. linearly independent ?

A: Given :123423571345

Q: 2 1 Let A = Show the details of two different methods [(1) using the adjoint and determinant, (2)…

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Q: b c is 3. C a Suppose that the determinant of a matrix A =d Lg e f h j. Evaluate the following:…

A: In this question we have to find the determinant of various matrices which we can find out by using…

Q: 3. Let 1 0 1 A = 3 1 2 4 1 3 (a) Find the determinant of A. (b) Is A invertible? Why or why not?

A: Given, For matrix invertible, .Where  is determinant of matrix.

Q: Find the determinants of the following matrices and classify them as either singular or non…

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Q: 3 6 [12] (a) Find the determinant of A. Let A det (A) - (b) Find the matrix of cofactors of A. C =…

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Q: a a 3. Compute the determinant a a by using the row/column operations a a R, → R, + R, + R, C, →C,-G…

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Q: 1. [3 pts. each] Let X and Y be 3 x 3 matrices such that det(X) = 3 and det(Y) = -7. Compute the…

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Q: 1 -11 -6 4 A = -3 2 3 4 0 1. Find the determinant of matrix A. Show your work step by step for full…

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Q: Calculate the determinant of matrix A with respect to the first, second and third rows. Show your…

A: Given Det(A) = ∑i=1n-1i+jaij|Mij| Solving for each ij

Q: 1. Given the equation: 1 1 + -= 1 x y (1) (a) Find by applying implicit differentiation in eq (1).…

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Q: 1 5) Let A= 1 -1 TON 0 2 0 -1 3 -6 a) Find A-¹. b) Find det(A), that is, the determinant of A.

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Q: Q1: The determinate of Matrix A is: * 3 -2 A=[1 4 0.5] 2 O (a) 16.5 O (b) 1.5. O (c) 11

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Q: -1 9. 1 8

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Q: can you explain more about how you get fxx, fxy, and fyy

A: Given: The given function is Px,y=e9x+10y-x2-y2-33. Also,  Px=9-2x·e9x+10y-x2-y2-33…

Q: -5 +- [55] 6 -3 (a) Find the determinant of A. det (A) = C = Let A (b) Find the matrix of cofactors…

A: A=-556-3 Note: We are allowed to solve three subparts at a time.

Q: Example C The following two functions are linearly independent: Yk (2) = e rọk, 0 = constant. (4.99)…

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Q: ах bx ах bx Vronskys determinatof functions , e, e хе хе

A: Vronsky's determinant: The Vronsky's determinant of a functions f1,f2,..., fn is given by,…