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: Let B = {(1, 3), (-2, –2)} and B' = {(-12, 0), (-4, 4)} be bases for R2, and let A- [:] 0 3 2 4 be…

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Q: (c) (e) 0-3 2 3 along the second column -1 0 1+i 2 -2i 0 1-i 3 4i 0 along the third row (d) (f) (i 0…

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Q: 1 1 1 -2 det(A) =det 1 0 -2 = 4 det(B) =det -1 -1 =-1 0 2 -1 Using the properties of determinants…

A: Given: det(A)=det11010-2020=4 det(B)=det10-20-1-10-10=-1 To determine: The value of d=det2B-1ABT…

Q: The function f : R³ → R' is linear and f(1,0, 0)) f(0, 1,0)) f(0,0, 1)) -1 5. (a) Find the matrix A.…

A: We will use the fact that the columns of A are images of basis vectors of the domain under f.

Q: et T: R³ → R³ be defined by T(x, y, z) = (x + y,x – y – 2,x + z).

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Q: 1-X 3 2 - X 3 - Consider the matrix 1 where A is a real number. (i) Find the determinant 2() of the…

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Q: 5. (a) Let 10-1 1 -1 -1 -1 1 P = 0 1 1 -1 2 -2 2 2 Evaluate the determinant of P. [4] (b) Suppose…

A: Step 1:Step 2: Step 3: Step 4:

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: -1 Find the determinant of matrix A det(A)

A: Solution

Q: Evaluate the determinant of the matrix A by inspection

A: I listed two methods to find determinant.

Q: (a) Evaluate the determinant of 1 1 1 A = 1 S 1 s? t2 (b) Find the values of s and t such that A is…

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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 1 -2 det(A) = det -2 = 4 det(B) = det -1 -1 =-1 0 2 0 -1 Using the properties of determinants…

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