If a, b, c are in A.P., then prove that the following are also in A.P. (i) a²(b + c), b²(c + a), c²(a+b) 1 1 √o+√ √e+√a' √a + √b CJCICH b С a (iii) a b + a b

Q: 9.) Simplify 5a2+ a2+ 7a a. 5a2+7a b. 6a2 + 7a c. 12a2 d. 13a3

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A: Consider a complex number z=a+bi Then, the complex conjugate of above complex number is given by:…

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Q: If a, b, c are in A.P., then prove that the following are also in A.P. (i) a²(b + c), b²(c + a),…

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Q: Hiw.sLetAzi+j-2K,b=-i-k and c=zi+uj-zk,finds t Ax(B+C)- 3 CA-B)xC s-(AXB)ec 2- A (2B-c) 4-2Ax 3B 6-…

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Q: 1. (a) Prove that if alb and alc. then alb² + 10c + a.

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Q: 2. Factor. a) 4-8x b) 9mn - 12n c) 6x2 - 5x

A: According to our guidelines, In case of questions with multiple subparts we are supposed to answer…

Q: リ ー上 5, Use the inverse imatirice s tofind and (24) 22 3 ミ 3. 3. 3 -2

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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: Problem no.3: Use Simpson rule’ 1/3 Method with (n = 6) to compute the integral below: 1.3 5x e-2x…

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Q: 3) Find integers x and y such that 13x + 15y = 1.

A: We see, 15 - 13 = 2              => k(15 - 13) = 2k for any integer k              => 15 k -…

Q: - [a C b If A = where a, b, c and d are real numbers, then prove that A²-(a + d)A + (ad-bc) I=O.…

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Q: 2. Show that a. Q(√5, √-5) = Q(√−1, √5) b. Q(√2, √6) = Q(√2, √3) c. Q(√5, √7) = Q(√5 + √7) d. Q(√a,…

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Q: -1] 0 is -1 01 The (1,2) – entry of5 3 3 l1 A) 14 B -1 c) 4 D) 1

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Q: Let A = 1 3 0 a) A-BT -4 -3 8 5 and B= = b) -3B12+2A32 c) B₁* A*2 -2 3 -1 -1 4] -2 10 7 · Calculate…

A: a)A−BT=⎣⎢⎢⎢⎡​424−4​−7−1−2−2​⎦⎥⎥⎥⎤​ b)−3B12​+2A32​=19 c)B1∗​.A∗2​=23Explanation:

Q: a) b) ab ac a + bc 3a 3 26 2. d) 1+ 2x 3x 똥 +

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Q: Let p, q be positive real numbers such that p + q = 1. Show that P√√x + √x₂ = √px1 + 9x₂. <a tax

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Q: a+2b 2 Let W = :a,be R}. Show that -4 lies in W. 2a -1

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Q: (d) Show that 1 + √2 is a unit in R and use this to conclude that R has infinitely many units. (e)…

A: To show that 1+2 is a unit in R , we need to find its inverse in R. Let a+b2 be the inverse of 1+2…