Prove: a) P(AnB) = P(A) + P(B) - P(AUB) b) P(AnB) = P(A) - P(A-B)

Q: a) What is P(ANB)? b) What is P(BA)? Suppose P(A/B)-0.2, P(B)-0.8, and P(A) - 0.64.

A: P(A|B) = 0.2P(B) = 0.8P(A) = 0.64

Q: Proved Ax (BNC) = (AX B)n (AXC) %3D

A:

Q: Given A= 7 2 80 and B= - 2 3 find: a) A+B, b) A-B, c) 2A+5B

A: We need to find out the values as given.

Q: (1) Cov(B1, yı) (2) Cov(Bo, Y1) (3) Cov(Bo, j)

A: Let Y = β0+β1X+εi be a linear regression model with the distribution where β0 = Y-β1X¯  and β1 =…

Q: 90 1) Let it be 2P + 50 = 2C2, then the value of n is: c) 7 b) 5

A:

Q: Q) find Projs ぶっi+) +3K, 5こてi-j+k

A: Given vector is : a→=i+2j+3kb→=2i-j+k To find the projection of b→ on a→.

Q: Show that PLEU FUG) = P(E) + P(F) + "P(G) - PLENF) - P(ENG) - P(FNG) + P(ENENG)

A: There are three events. These are E, F, G. The objective is to show that,

Q: Prove : (A-B)n C =(A n C) -B

A:

Q: Evaluate (2i)3 a) 8 b) –8 с) -8i d) 8i

A: Let z=(2i)3

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

A:

Q: Given P(A|B) = 3 P(A|B°) , P(A) = 0.02 and P(B) = 0.25 a) Find P(ANB) b) Find P(B|A) c) Are A and B…

A:

Q: Evaluate SA(u) du if A(u) a) 6i+8k b) -6i+8k c) 61-8k (3u²-1)i + (2u-3)j + (6u²-4u)k. d)-61-8k

A:

Q: IEvaluate Ax)-2x+3x-4 A) x-3 B) x-h+/

A:

Q: 16 If X-B (4, p) and P (X=0)=- then P (X=4) 81

A:

Q: 10-2)3 62 ÷ 65

A: We have to find As per guidelines we have to solve three subparts

Q: If C(s)=16-2s2 then find a) C(3) b)C(-2) c)C(-1)

A:

Q: 10) Prove the following statements true or false: i)āx(bx?) = (āxb)xã, ii)(a + b)x(ã − b) = 26 xã

A:

Q: I only need answers to (a) (b) (c)

A:

Q: Provide an interpretation which is true and one that is false. (∃ x)(P(x,b))

A:

Q: ´5s²–15s-11) -(s+1)(s–2)³. 34-2s 2. i) Find ii) Evaluate (15(s-5)(s+3).

A: The solution is given as

Q: If n(A) = 115, n(B) = 115, and n(A U B) = 140, what is n(An B)?

A:

Q: Find the value of n(An B) if n(A) = 10, n(B) = 13, and n(A U B) = 18. n(An B) = (Type a whole…

A:

Q: Find |AT|, |A²|, |AAŢ|, |2A\, and |A¯¹]. 4 03 A 2-1 5 1 46 (a) IATI (b) |A²| (c) JAATI

A:

Q: (b) Prove (or show) that Hint: Start from % = 0² ( 1 + TH SSTT = Var (Bo) = Var(y - B₁) = Var(ÿ) +…

A:

Q: Let a = (5, – 3, 6) and b = (5, 3, 4). (a – 6) × (ã + 6) -| X (a +

A: Given: a→=5,-3,6and b→=5,3,4

Q: a) 1 (x-1)(x+2)(x+4)

A:

Q: 2. If p = 41+2j – k, q = 6i+ 6j– 2k and 7 = -3i – 4j– 3k, evaluate a) q• (p- 2r) b) (r +g• p) c)…

A: Here we use formula of dot product of two vector, and addition, subtraction, multiplication of…

Q: D -7 = -9+ V12 – a 2) 0 = 4v-6 –n 3) 7v12x + 4 = 56

A: Given equations are  (1) -7=-9+12-a (2) 0=4-6-n (3) 712x+4=56

Q: Simplify the expression Y = bar((AB + bar C) (bar (A + B) + C)) Obtain the canonical product of sum…

A:

Q: if ACB, P(A)=1/4, and P(B)=1/3, find P(A/B) and P(BA)

A: Given A⊂B  P(A)=1/4, P(B)=1/3

Q: 1. (2ab)3 Ob) 2ab3 Oa) 8a3b3 O d) 6ab O ) 6a b3 Simplify:(x*Xx?) 2. O b) x6 O a) x5 O d) x1.5 O C) X

A:

Q: Q6) Show that if P(AU B) C P(A)U P(B) then either A C BV BCA. Justify your answer.

A: The solution are next step

Q: Prove that A-B=An(-B) = (-B) – (-A) = −[(-A) U B]. Also, give three expressions for An B and AU B,…

A: Difference of sets: Given two sets A and B, the difference A−B is defined as the set of all elements…

Q: actortise the expression: a^(2)+by^(2)+bxy +axy

A: Given expression: ax² + by² + bxy + axy

Q: а) In(x) — 3(Vinx) + 2 — 0 b) 25% – 8(5*) = -16

A: lnx-3lnx+2=0

Q: Ba, "Vx(Fxa →3yBy) v VxFbx /:: Ba & Fba Prove this statement

A: Sol

Q: fo = 19, fi = -23, - 2 fn = - fn+1 + 15 fn-1 %3D The following four questions are all based on the…

A:

Q: Find the convolution of e3u(t) and tu(t). Answer: + _ + -+) u(t) Find the convolution of e3tu(t) and…

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.