2. Verify that det(AB)= det(A)det(B) and determine whether the equality det(A+B) = det(A) + det (B) holds. [2 A= |3 Lo 4 -1] 5 4 11 | B= | 6 -2 1 -3 5 21

Q: 29. Compute det B, where B = 1 2 2

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Q: 2 Let A= then det(3A") = 6- -2 - 18 -6

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Q: Compute A?x and A3x the correct way: ´1 0 () 0 1 A = 3 0 2 0 1 1 1

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Q: verify that det(AB) = det(BA) and deter- mine whether the equality det(A + B) = det(A) + det(B)…

A: See the attachment

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Q: 49. Prove that x +> 2 (x1/2 – x-1/2)2. 2 for all x > 0. Hint: Consider

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Q: 3. prove that: det (AB) = det (A) det (B) If a - (;). » - ( :) 2 -1 7 A = 3 2 4

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Q: EX+ Prove that [X Ju cx)] = x'Jr-, cx) Solp 2. ヘャut 2m+2V (-1)" X 2m+V (m!)P(m+v+1). neno 2m+2U-1…

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Q: Compute AB, where A AT B = = 24 09 4 -3 -1 and B = 76 (1 %). 6 4

A:

Q: a) Ho:μ=2 Ha:μ>3 b) Ho:x̄=0.7 Ha:x̄<0.7    Are these null and alternative hyothesis correct

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A: Here  A =x∈Z| x=5a+2 for some integer a ,B=y∈z|y=10b-3 for some integer b    C=z∈Z | z=10c+7 for…

Q: Show that the following argument is invalid by providing a counterexample: \xQ(x) 3x (-P(x) ^ Q(x))

A: We are given the statement ∀x Q(x). Now, we need to show that the conclusion ∃x(¬P(x)∧Q(x)) is not…

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Q: 2.1. Prove that B Is erse of A -17 11] -7,B: 0 3 2 [1 1 2 2 4 -3 [3 6 -5] 2 A = -1 11

A: To prove that B is the inverse of A.

Q: (b) Use the value of det(A) to evaluate 1 2 3 3 -2 3 3 1 1 1 2 -2 -3 -1 4. 1 3 -2 4) 2. 2. 021

A:

Q: Let A = -[-32-3] and B = (a) Find AB, A-1, and B-1. AB= 5-3 2-1 A-1 B-1 = (b) Show that (AB)-1 =…

A: a)AB=2-2-235-32-1AB=2(5)-2(2)2(-3)+2-2(5)+3(2)-2(-3)-3AB=10-4-6+2-10+66-3AB=[6-4-43]A-1=1AAdj(A)A-1=…

Q: 2 Let A = then det(3AT) - 18 -6 -2 II

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Q: 11.32 question attached. Thank you for answering my question!

A: It is given that X and Y are independent normal random variables.The required probability is:

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Q: Evaluate O a. 2/ + 3+ 3-6ln |z/+1|+C O b. 2 3T+ 32 +6ln r/ +1+C O c. 2vE - 3T +322 – 6ln |z'/0 –…

A: ∫1x+x3dx

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Q: verify that det(AB) = det(BA) and deter- mine whether the equality det(A + B) = det(A) + det (B)…

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Q: Show that: If |z| = 2, then: z* – z2 – 4| Re < 6 z + 6

A: A complex number z=x+iy are graphically represented as (x,y) on coordinate plane. The polar…

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A: Given A=112231-124, B=230-13-352515715-15115

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A:

Q: If z̟ = 1 + jb , z2 = re¬j² , z1/z2 = -10, determine all possible values of b and r.

A: According to the given information, it is required to determine the possible values of b and r.

Q: If A is a 2 x 2 with det(A) = 3, then det(4A1) = %3D

A: det(A-1)=1det(A) det(4A-1)=4ndet(A-1) where n is the order of the matrix.

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A: This question can be solved using the concept of multiplication of matrices.

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Q: 3. prove that: det (AB) = det (A) det (B) If 2 -1 7 2 B = A 3 2 -3 4

A: In the question it is asked to prove the property det(AB)=det(A).det(B). Where A=2-132 and B=72-34

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Q: 21 41 Verify the following directly if A = 1. B = |; .c = [, а. A(ВC) %3D (АB)C b. А(B+C) %3 AB + AC…

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Q: 53. Suppose that a + 0. (a) If a · b = a·c, does it follow that b (b) If a X b = a X c, does it…

A: Given a, b, c are three vectors and a ≠ 0.

Q: 6. Prove that, if a, b e Z, then 3a? – 4b – 5 0. - -

A: Answer

Q: Show that r(r+3) Hence, Show that 1 +. 2.5 1 1-4 3-6 n(n+3) n+3 n+2 n+1

A: Using series

Q: R is commutative if and only if R[x] is Commutative. True or False

A: The given statement is true. If Rx is cummutative.So, R⊂RxRx is cummutative.R is also…

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A: Please refer the attached image for complete solution.

Q: X Compute A*; Btr BA,(BA tr BA, (BA)O [ - 5 -4 I B -a 3 -3 5

A:

Q: 1. If f(x) = x- 1 and g(x) = x2 – 2x + 1, then (g -f)(x) =? 2. If p(x) = 2x2 - 2 and q(x) = *, then…

A: Composite function:f∘gx=fgxArithmetic combination:f+gx=fx+gxf-gx=fx-gxfgx=fx.gxfgx=fxgx ;  gx≠0

Q: Then prove that 3 (i) P (AUB) > 1 (ii) <P (An B) S 10

A: Answer: From the given data, P(A) = 3/5 and P(B) = 1/2

Q: 0 1] -1 3 -2 0 0 1 Compute det (B), where B 3 det (B*)

A:

Q: 0. Prove that (i) |4' ||, =||4||,, and (ii) ||4' A|| -||4|-

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Q: D. Is there guaranteed to exist a value of x = c on -2 < c < 2, such that h'(c) = 0? Give a reason…

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A: To Show: ∫0πdθa+bcosθ=πba2-b2 Concept: i. 1+tan2x=sec2xii. cos x=1-tan2x21+tan2x2iii.…

Q: 2. Determine the products C = AB and D = BA if %3D %3D 4 61 -7 A = 1 -5 -1 3 -5 2 %3D -9 --13 -4 7 6…

A: The given matrices are A=46−7−51−9−3114×2 and B=−13−52−13−4762×4.

Q: (16) Show that AB=BA for 1 5 0 0 A = 0 3 0 0 0 and B = 3 1 2

A:

Q: Prove that Q (1 + i) belongs to Q (4-i)

A: Prove that Q (1 + i) belongs to Q (4-i)