Let where A and B are some constants. given that ü = < A + 2 B, A - B, A +B>, V =< 3 - 2 A, B + 3, A- B> ü + 10v = < - 38, 70, 8 > find the value of the product AB

Q: 2 and B= 1 0. then Show that if A = 6. -1 2 (A + B)(A + B) # A² + 2AB + B?

A: Given that A=-1201 and B=10-12 We have to show that A+BA+B≠A2+2AB+B2

Q: Evaluate if x=4,8,3,-2 ∑x ∑x+1 ∑(x+1) 3∑x - 4

A: Given that  if x=4,8,3,-2

Q: If possible, write -1- 12x8r² as a linear combination of x -x², 2x + x² and 2x 1 + x². Otherwise,…

A: Let U={u1,u2,⋯,um} be m vectors of a vector space V. Let v∈V(F) then v can be expressed as linear…

Q: 4. Simplify 3(8z+2y). O 24z + 2y 24x+2y D24x+6y 30z +y 30cv

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Q: A(1,-3),B(1,1),C(5,1),D(5,-3) translation of 3 units left and 5 units up.

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Q: b2 over b-a + a2 over a-b

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Q: 12y+x=-3y+5x-6 Put in standard form.

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Q: Ifv = [ -2, 4], compute and draw 2v, 1/2 v, and -2v.

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Q: 4x+2y=2 1.) 2x+2y=4

A: The given system of equation is: 4x+2y=22x+2y=4

Q: Find u × v, v × u, and v × v. u = (3, 2, 8) v = (−3, −1, −9)

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Q: Determine all values of the constants a0,a1,a2, and a3 such that x3+2x =a0P0+a1P1+a2P2+a3P3.

A: We are given the following equation: x3+2x=a0P0+a1P1+a2P2+a3P3 Our aim is to find the values of all…

Q: Add. (-9 + 5x6 + 6x4) + (6x6 - 2x4+7) O 11 + 4x6 - 2x² -3x6 + 3x4 + 13 11x6 + 4x4-2 O 4x² O 13x10

A: Add:- (-9+5x6+6x4)+(6x6-2x4+7) Sol:- -9+11x6+4x4+7 11x6+4x4-2 So, third option is correct.

Q: Find a and b such that 2 1 20 = a 2 +b -4 -22 -1 a = b =

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Q: Express 4 as a linear combination of 72 and 104. Find x and y such that 4=72x+104y

A: We have to express 4 as a linear combination of 72 and 104  That is, we have to find x and y such…

Q: Multiply. (3ử– 6u+4)(5u-7) -би+ | Simplify your answer.

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Q: Find u+v-2u. U= = (5, 3) and v = (-3,5) u+v-2u=

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Q: Find a and b such that a = 9 = 0 - a -1 +6 10 6

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Q: -5 4x If possible, write -5 - 4x - 2x² as a linear combination of 2 - x + x²,-2-x² and x - 5 2x².…

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Q: Find +62+7) dr 1(2²³/20 +C

A: Integration  ∫3x2+6x+7dx

Q: Evaluate A- using the method of adjoints 3 2 7 -3 3 4 1 A = 1 -4 -3 -4 1 -2

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Q: sinh e Incot3x h- dx St 1+9x²

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Q: z - 8 j, k, 64y3 + 125 I. -60x² +315x - 75

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Q: 10. 3 + Зу- 1 + у

A: Given that                     3+3y-1+y Now we simplify this.                           3+3y-1+y…

Q: Find a × b if b = (–6, 9, —15) and à = (4, −6, 10) (-3,-2,0) (0,0,0) (1,-1,-1) (-24,-54,-150)

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Q: If a = (2, -1, 4) and b = (8, 2, 1), find the following. a × b = -9,30,12 X bx a = -9,- 30, - 12

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Q: Perform the addition and simplify. (12y* – 4y² + x² - 4) + (- 5y* + 6y² + 10) (12y* - 4y? + x? - 4)…

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Q: If possible, write -6- 19x - IIx" as a linear combination of -1 - -619x11x² = (-1-x-x²)+ (1 + 2x +…

A: Write -6-19x-11x2 in the linear combination of -1-x-x2, 1+2x+x2 and -1-3x-2x2.

Q: -2 1 21 = a 3 +b -3 -22

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Q: write of linear Combination as a V,Vz, V3 where V= (2,7,10), V.=(1,2,3),V2=(1,3,5), V3=(1,5,9)

A: Let us assume v can be expressed as linear combination of v1, v2 and v3 v=av1+bv2+cv3…

Q: JIT x²-2y+xz) dydzdx= -2°1 .A 27 4 .B 17 4 .C 27 4 .D 17 4

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Q: 2 If possible, write 7 - 4x 6x² as a linear combination of -2 - x + x², 2 x + x², 2x² and 1 + x.…

A: We have to find the values of a, b, c such that,7 - 4x - 6x2 = a(-2-2x + x2) + b(2-x2) + c(1+x)