Q1) Find an LU factorization if: 2 -4 -2 7 6 -9 -5 8 I. A= 2 -7 -3 9 4 -2 -2 -1 -6 3 3 4 2 0 5 | A= -6 3 -13 -3 9 16 17] 2 II. 4 9 -

Q: Since b =2i ̂-j ̂-3k ̂ and c =i ̂-5j ̂+k ̂, what is the result of ( b . c )?

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Q: Show that: If |z| = 1, then: z' + 4z + 5 z2 + 5z + 6

A: Given: z=1 Then show that: z3+4z+5z2+5z+6≤5

Q: (b) Prove or disprove: Z10 ~ Z5 x Z₂.

A: We shall solve first question only as you have asked more than one unrelated question. For others…

Q: Verify that (AB)T = BTAT.

A:

Q: Verify that (AB)T = BTAT.

A:

Q: 1. Write out the dual of: a. Min 3xl + 2x2 + x3 s.t. xl + x2 - x3 = 4 2x2 + x3 < 7 -xl + 3x2 2 6 х1,…

A: The given LPP is: Min 3x1+2x2+x3 Subject to x1+x2-x3=42x2+x3≤7-x1+3x2≥6x1,x2,x3≥0

Q: Show that =- 5)" /31 + 6. 1 = 2 ) /7! + () /9! – ... %3D | -- IN

A: We know that, from the Taylor's formula for power series expansion of sinx is given as…

Q: 1. Find the 5roots of z1 = -V3+iv3. %3D

A: (As per bartleby guidelines, for multiple questions asked, only the first question will be solved.…

Q: Prove that if |z| = 3, then %3D 5 2z – 1 7 - 13 4+ 22

A: The given is related to complex numbers. The solution is explained below.

Q: Use the given LU factorization to find all solutions to Ax = b 0 5 1 0 0 15 A = 4 1 0 0 -2 |, b 54…

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Q: Differentiate the following by using product rule. (9x2-2)(3x+1) (3x+10)(6x2-7x)

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Q: Compute A B, where A = AB= -5 6 -5 0 and B = 6 7 2 9

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Q: b)Show that, 6(z, 3zy – y' and (z,y) = -+3ry are harmonie

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Q: How did they calculate what T does to the elements of B?

A: You want to know "How did they calculate what T does to the elements of B?" We have  B=1, x, x2, x3…

Q: 2. Compute the value of | V25–x² dr

A: Given data:   The given integral expression is I=∫0525-x2dx.     Assume x=5sint, and differentiate…

Q: Express y as a fiunetion af k if y - 2r+5, 1- V3t -1, and t- 3k - 5.

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Q: Show that 1/3  Tn +  2/3 Mn  = S 2n

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Q: В. a = lass)-(21-1) given that w= In(6x + 2y³ – 3z).

A:

Q: Suppose an = 5an-1+4an-2 – 3an-3 and a4 = 22, аs — 127, and ag = 717. Find a1, a2, and аз. ai = a2 =…

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Q: Suppose X has n elements and Y has m elements. How many bijections X → Y are there?

A: To find: The number of bijections X → Y are there. Given information: X has n elements and Y has m…

Q: what is the characteristic of Z6xZ9

A:

Q: Does S = {x² + 1,x² – 1, 2x – 1} span P2?

A: we know dimension of P2 is 3 so any set which span P2 must have at least 3 elements. here given set…

Q: Q2.2 Compute 3 -7 2 3 3 -3 det 3 -8 2 - 3 2 2 (Entor the

A: according to the guidelines we should able to do only one question at a time #2.2

Q: or what values of the constar - 3 y- 2 k z+1 글 -꽃 lie in the 4

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Q: Find the product of x and y if x, 3/2, 6/7, y  are in G.P

A:

Q: Show that 3n2+8nlogn is big-Oh (n²)

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Consider a LU factorization of -2 1 3 A = 1 4 -2 -5 as A=LU. Then L2,1 and U1,1 are respectively…

A:

Q: The Cholesky factorization of 53 is UTU where U is: 3 2 V5 5 -3 V5 1 3. 0 1/5] V5 5 3 0. 1

A: The given matrix is,5332

Q: Compute A−2 two different ways and show that the results are equal.

A:

Q: Fiven with z1 = (-3,1) and z2 = (1, 4). Show that |21 2| = |21||2|- %3D

A: Complex number and it's modulus

Q: Differentiate the following (choose two only )( 5 .. ) 1)2xsin-13x x+1 2)y = In Vx-2

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Q: Z4×Z6 has an element of order 24. true or false ?

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Q: 18. Find mZBCA. B (5x+12)° (9x +1) (10x-37)

A: From the given figure find out m∠BCA

Q: What is the midpoint between z1 = 9i and z2 = 4? (2, 4.5) (-4,-9) (-2,-4.5) (4, 9)

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Q: Compute A−2 two different ways and show that the results are equal.

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Q: 11 ,5 -2d*¨f -2 2 4df

A:

Q: What is the midpoint between z1 = 3 + 9i and z2 = 4 - 12i? (0.5,-10.5) (3.5,-1.5) (-2,-2.5) (6,-1.5)

A: Explanation of the answer is as follows

Q: b) Prove or disprove: Z10 ~ Z5 x Z₂.

A:

Q: Consider a LU factorization of 3 A = 6 as A=LU. Then L2,1 and U1,1 are respectively equal to

A: solution:-

Q: Show that |Aut(Z2 × Z2)| = 6

A:

Q: Show that: If |z| = 1, then: |z3 + 4z + 5 < 5 z + 5z + 6

A: Given: z=1 Then show that z3+4z+5z2+5z+6≤5

Q: Show that  1/3 Tn + 2/3Mn ) = S2n.

A: By definition, Tn=12∆xfx0+2fx1+....+2fxn-1+fxnMn=∆xfx1+fx2+.....+fxn-1+fxn…

Q: what is the multiplicity of -1 in x^4-2x^3-3x^2+4x+4

A:

Q: D. Let Find 2,-

A: We will find out the required value.

Q: Use Giramer Rule to Find ,z -2x + 33-Z = 1 メ+29-2-4 -2x -+7 = -3

A:

Q: List the sides of AFGH in order from least to greates if mZF=(5x+6)°, mZG=(12x-4)°, and m…

A: Consider the following △FGH: m∠F=5x+6°m∠G=12x-4°m∠H=4x+31° Sum of all angles of triangle is 180°.…

Q: 1aar = |1a – 1g| AAB ΑΔΒ

A:

Q: Consider a LU factorization of 3 A = as A=LU. Then L2,1 and U1,1

A: We have to find values given in the question from the matrix.

Q: 16 3. Show that for x2 + 2xy - 3y² = 4, y" (x-3y)3

A: We will find y" as following.

Q: b If K = 4.1 x 10-6 then pK, Submit

A: This is a basic log problem

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.