verify that det(AB) = det(BA) and deter- mine whether the equality det(A + B) = det(A) + det(B) holds. 2 1 0 5. A =3 4 3 and B =7 1 2 5 1 8 2 6. A = -1 and B = 1 1 3. 3 -1

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

A:

Q: Prove the following fact: A" = 3"-1A. 1 1 1 1 1 1 1 1 1 A =

A: Given, A =111111111  We have to  prove An = 3n-1A

Q: (-1)"2" /ñ Prove that if m is a positive interger, 1'(-ni +3) =1:3.5...(2m – 1)

A: I will use method of induction to prove the statment.

Q: What is eh REF of B? 1 2 1 1 B = نه who 1 0 -1 به T NC vсы N 5 0 2]

A:

Q: 4. Show that there do not exist constants C1, C2 and c3 which satisfy: (1; -1; 4) = C1( 2; 3; 5)…

A: 4.1, -1, 4=c12,3,5+c2-1,0,6+c31,3,11

Q: 26) If x, y, u, v are variables connected by the relations 1 1 x? =au? +bv2, y² =au² –bv² where a…

A: Given, x2=au12+bv12…1y2=au12-bv12…2 Equation 1+2 gives:…

Q: Let z1 = 2+ j3 and z2 = 4 – j5. Evaluate 1+2 %3D 21-22

A:

Q: 3. Show that if A-1 exists, then f eAT dr = A-(eAt – I) = (e4t – I)A-1.

A:

Q: 3 Let A = -6 -1 -2 and v = -6- -2 3 Av = -6 2 -9 Ex: 5 s v in null(A)? Select an option

A:

Q: ADMATH 3. 1. %3D tise pawer senies I+x²

A: The given differential equation is

Q: Consider the following statements: 1. 27x +3,27€ - 11, and 27x + are antiderivatives of 27. II. In…

A:

Q: 1. CHAIN OF REASONING: F= -E-R -S E → W RvS WV-S

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: (b) Let aji aj2 _a]3 A= |a21 a22 a23 |аз1 аз2 аз3 2a11 2a12 2a13 and B = a11+a21 a12+a22 a13 +a23…

A: Given problem:-

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

A: Null hypothesis is the statement about the population parameter, such a hypothesis is usually of no…

Q: (d) The apartment is hot if and only if the temperature is not 75º and the air conditioning is not…

A: Here given Statement in English convert them to symbolic form using standard notation

Q: If u = x3 -3xy and v= 3x2y-y3, prove that Pu/Əx2 + Pu/əy2 = Pv/ax2 + Pv/@y²

A:

Q: (b) Let 2a11 2а12 2а13 |aji aj2 a13 A = а22 а23 and B= ajj+a21__a12+a22 _a13+a23 а21 |аз1 аҙ2 а аз1…

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Q: ne set {u1, u2, U3} is orthonormal. 1 2 V5 2 ,u2= 10 1 ,U3= 1= 10

A: The condition for the vectors to be orthonormal is that the  magnitude of each vector is 1 and the…

Q: 1 0 2 2 4 8 -7 9, then prove that (AB)' = B" A" . -5 0 If A = 2 -1 3 and B : 3 4 1 8 2

A: Evaluate (AB)T as follows.…

Q: In Exercises 1-4, verify that det(kA) = k" det(A). 1. A = ;k= 2 3 2. A = k =-4 37 1; k = -2 3. A =…

A: Explanation of the answer is as follows

Q: Show that e = (1 + i)/√2 if and only if z = (n/4+2km)i, k = 0.±1, +2...

A: This question is related to complex numbers,  we will solve it using given information.

Q: iken that I+2=1 xpressyin terms of xand z.

A: A function defines a relationship between two sets, where one set is dependent on other set. Any…

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

A:

Q: 3. prove that: det (AB) = det (A) det (B) a - (; ), » - ( ) 2 -1 7 2 B = 2 в 3 %3D

A:

Q: 1. Consider the following statements: 1 I. 27x+3, 27x - 11, and 27x+ are antiderivatives of 27. 7…

A:

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

A:

Q: Show that A and B commutes: * 2/3 -1/31 1/5 7/15 -1/5 1/15. 1 1 0. 21 1B =|-3/5 2/5 2 4. 3 %3D -1 ]

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

Q: a) If Z1 = -3 + 3i and Z2 = 4i. Show that: i) Arg(Z,Z2) + Arg(Z,) + Arg(Z2) ii) Arg (2) = Arg(Z,) –…

A:

Q: 44. (a) Let a, b, ceZ with (a, b) = 1 and a | bc. Prove that a c. (b) Provide a counterexample to…

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Q: -2 -24 Let aj = 3 a2 = -7 and b 30 -5 17 -65 Is ba linear combination of a¡ and a2 ?

A:

Q: Show that ∗ : R × R → R defined by        a ∗ b = a + 2b is not commutative.

A: Show that ∗ : R × R → R defined by        a ∗ b = a + 2b is not commutative.

Q: 1. Let z E C. Prove that Re(z?) = [Re(z)]? - [Im(2)]² and Im(z²) = 2 Re(2) Im(2)

A:

Q: If A, B are 3 x 3 matric det(AB ') = 12 and a Then det(3A". (B)¯1)

A:

Q: Let C ~ Cauchy(0,1). Show that C² + C-2 =9 4C² + 2.

A: c^2+1/c^2 &gt;2 thats why it is equal to 4c^2+2

Q: Prove or disprove set Is a substance of R3 y determing IF it passes each of the three parts.

A:

Q: 2. Verify that det(AB)= det(A)det(B) and determine whether the equality det(A+B) = det(A) + det (B)…

A: Note : As per the authoring guidelines, when multiple questions are posted, then only first question…

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

Q: Consider the expressions: f1 = (Ax.((Ay. (y x)) y) u) 12 = (Axx y) a. List the bound variable…

A: Given: Variables applied in a function that are neither local variables nor parameters of that…

Q: Prove that r(1/4) r(3/4) = /27. %3D

A:

Q: ao + 2a1 + a2 - azz²) = | da0 + 7a; + 5az 3ao + 5a, + 5a2, Let T(ao + a;7 - Determine ifT is…

A:

Q: Ux = Uy + u a²u 4 ax2 azu at2

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Q: The set {u1, u2, u3} is orthonormal. 1 2 V5 V5 1 2 1 2 10 ,U2= ,u3= 10 1 2 1 2 10 10 True False

A:

Q: Q1) Compute the products using the definition as a linear combination. 8 3 -4 1 2 1 5 1

A: As per the definition of linear combination abcdef.x1x2x3=x1.ad+x2.be+x3.cf

Q: Q4: 1- Prove that (1– i)? + (1+ i)² = 0 . %3D 2- Put in the form a + ib ((1+ i)²)² - ((1- i)²)².

A:

Q: One of the following is always true A) If det(A) = det(B), then det(A+ B) = 2det(A) B) adj(AB) =…

A: Solution

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: 3) Calculate: AВ-ВА , АС-СА , ВС-СВ Where 1 1 0 1 A 1 1 B -1 1 0 0 V2 Vzi 1 0. 0 -1 0. -1

A: I have found each product term one by one

Q: Prove that if c=12n+4 where n in Z then c is not a linear combination of 27 and 18

A:

Q: ieN 6. (a) Uto, i+ 1] = (b) N[0,i+1]= ieN ieN 7. (a) URx[i,i+1] = (b) ORXlii+1l=

A:

Q: 17

A:

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.