Prove that if A and B are similar, then Tr(A) = Tr(B ).

Q: Find AB such that [3 1 21 T-1 A = 2 1 2 and B =|4 [1 2 2] -2 -5]

A: The solution is given as

Q: Let A 1 value of k. [23] A and B = 1 -7 217 k If AB = BA, find the

A:

Q: [3 5. Let A = and B = [, Find C = (AB)"

A: In the given matrix, A and matrix B  Apply matrix multiplication technique .

Q: If P(A) = 0.5, P(B)= 0.40 and P(A U B) = 0.70, find P(A/B) and P(A U B) where A is the complement of…

A: HERE GIVEN, p(A) = 0.5 p(B) = 0.40 p(A ∪ B) = 0.70

Q: E (ax, + by, + c) =

A: Let (x1, x2, x3, ..., xn) and (y1, y2, y3,..., yn) be finite sequence of numbers of the same length,…

Q: 2. Let A = 201-18 and /= 2 1 1 2 01 Find A(A+1).

A: A=[2 1      1 2]I=[1 0      0 1]

Q: 3. Check that in each of the following cases, the equation F = 0 defines y locally as a C' function…

A:

Q: Let ā = (2, 3, – 2) and b = (4, 2, – 2). - Find a · 6.

A: The dot product of two vectors is calculated as follows: a→·b→=xi^+yj^+zk^·ai^+bj^+ck^=ax+by+cz

Q: (a) Let n be any integer. Prove that n2 is congruent to 0, 1 or 4 modulo 8.

A: Note: According to bartleby guidelines we have to answer only first question please upload the…

Q: Suppose a time series of returns r, follows the following recursive formula: = (1 — αL)(1 — BL³) at…

A: The question presents a recursive formula for a time series of returns, denoted by rt, which…

Q: if fcx) = _X then f (-1) is: |-X

A:

Q: Show that if AB = I, then det(A) 0 and det(B) # 0.

A: Here given as AB=In find determinant both sides detAB=detIndetAB=1

Q: ,3), calculate the value of a it the

A: We have to find the value .

Q: Show that (a + b)x = ax + bx for all a, b E F and all x € F¹.

A:

Q: Which set of measures could represent the lengths of the sides of a right triangle? O 7,17,24 O V3.…

A: Properties of right angle triangle: 1.  The  longest  side is the hypotenuse. 2.  (base)2 +…

Q: 0 500 soft ( + ( ① so) & cu!ss) d + ) (cose) dr

A:

Q: andom sample of measurement a populabion with population standard deviation a,3 had a sample mean of…

A: Given: Sample measurements from first population n1 = 49 Sample mean of first population x¯1 = 9…

Q: Engineers at a tire manufacturing corporation wish to test a new tire material tor increased durabl…

A: Let xi, (i=1,2,...n) and yi, (i=1,2,...n) are two samples of same sizes and these two samples are…

Q: Show that (AB)T and BTAT are equal.

A: Now,

Q: 2. Let T=

A: Given that, T=22-1-163201 We have to find adjoint T.

Q: 1 의( (eat – ebt)} = %3D la-b (s-a)(s-b)

A: Here we have to prove that,  L1a-beat-ebt=1s-as-b

Q: 2. Find A if (A-1-21)² = -2 = -21]

A: Basic properties of matrix are used

Q: Let 1 3 A = -2 -1 and В - 2 -2. a. Find AT and show that (A")' = A. b. Show that (A+B)" = AT + B".…

A:

Q: d. Use your work in (a)-(c) to evaluate the indefinite integral f sin³(x) dx. e. Use a similar…

A:

Q: If A = {–1, 1}, find A × A × A.

A:

Q: Ε[βο] = βι

A: We have a linear regression model y = Xβ + ε, where y is a vector of responses, X is a matrix of…