If 3 1 0 A = | 5 2 -1 1 4 - 2 The adjoint of A is -1 1 9 9. 18 - 6 3 -11 – 11 1 True False

Q: Let [1 2 21 A = 1 1 -1 0 and U = |-2, then determine if 3 -1 2 (i) U is in Nul A. (ii) U is in Col…

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Q: 3. Prove that (An B)² C A × B.

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Q: Prove let B= 6+ I %3D : m = ',2,3, 3m S. Then inf(8) =6

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Q: Show that if AB = AC and A is nonsingular, thenB = C.

A: Given that  A is invertible matrix. It means inverse of A matrix is possible. A is non-singular…

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: * If Iz| = Re(z), then z is

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Q: I, \B|, A + B, and |A + B|. Then verify -1 1 8. 1 0 1 A = 0 1 1 B = -1 1 8 1 1 -1 0 1 8

A: Given: A=-11801111-1, B=101-118018

Q: Let -2 0 A= -3 1 Find A-, if it exists. 1 2 а) 3 1 2

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Q: Let M = {-x² + 2,x + 1, 2x}. %3D Which of the following statements is true about M?

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Q: If z, = 3+2). z, = 4 - 8j and z, = 2+5j , find the conjugate of: (a) z, + 22 (b) z, -z, (c) z, (d)

A: Given, z1=3+2j, z2=4-8j & z3=2+5j To find conjugate of, (a) z1+z2(b) z1-z2(c) z1z2(d) z3z2

Q: -1 If A=A,then A must equal to either I or -I. Select one: True False

A: Given statement is A=A-1, then A must equal to I or -I

Q: Show that 1-r for any r 1 1 and any 3. nEN

A: answer

Q: Which of the following is equivalent to csc^2β(secβ−1)(secβ+1) for all values of β for which…

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Q: Prove that ∀a, b, k ∈ Z that ((4|k) ∧ (k = ab)) ⇒ (2|a ∨ 2|b)

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Q: (a) Show that if (a,342) = 171 and (b, 342) = 171 then (a+b,342) = 342. %3D %3D (b) Show that if (a,…

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Q: ) If In(a) = 2, In(b) = 3, and In(c) = 5, evaluate the %3D ollowing: -1 a a) In b-4c! 5) In Vbºca¬T…

A: Answer (a):   lna-1b-4c1= ln(a-1) - ln ( b-4c1)                                            =ln(a-1)…

Q: 2 2 22 if== prove that 22 a¯x +b¯y¯ +c¯=¯ 3, ,3, 3 a'x + b°y +c°z xyz abc %3D

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Q: Prove: If a > b > 0, then 0 < 1/a < 1/b.

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Q: If then the dimension of AB is and the dimension of BA is B = A = 7 0 -5 3 6 4 -2 -2 -5 4 3 -9 -2 0…

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Q: : let u (1, 2, 3), v = (2, 2, -1) and w = (4, 0, -4) then u-v + 2w equal %3D (7, 0, 1) O None O…

A: Calculate u-v+2w:  u-v+2w=1,2,3-2,2,-1+24,0,-4                  =1-2+2·4,2-2+2·0,3--1+2·-4…

Q: The transitive property of congruence states that if 2 A = ZB and z B C, then A C. O True O False

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Q: Which of the following are indeterminate forms? 00, 00, 0“, 1º, ∞* Select one: O a. 00, 0º. 0*, 1º,…

A: We will solve the problem

Q: Prove the following theorems: 1. If a /b, then a / bc.

A: Suppose that a | b. If a|b, then by definition there exist an integer m such that b=ma. That is,…

Q: 9. Use the adjoint of A to find A', where -1 3 A =0 -2 1 -2] 1 Confirm your answer by showing that…

A: A=-1320-2110-2

Q: 3. Show that 1 > 0. 4. Show that if a > b and c < 0, then ac < bc.

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Q: If X ∼ N (μX , σ2X ) and Y ∼ N (μY , σ2Y ) are independent, then prove X + Y ∼ N (μX + μY , σ2X +…

A: X~Nμx,σx2 and Y~Nμy,σy2 are independent. Here, X~Nμx,σx2. In this context, it is known that the…

Q: Q.31 If a+b+c=5 and ab+bc+ ca=10, then prove that a +b³ +c³ – 3abc=-25 Q.32 Prove that :

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Q: Prove: If a &lt; 0 and b &gt; 0, then | a  + b | &lt; | a | + | b |

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Q: Which of the following is correct? ai II-1 b; O IIE, a;b; = (a1+...+an)(bı+...+bn) O II, a;b; =…

A: As ∑is used to denote the sum, similarly, ∏is used to denote the product. Assume, a be a variable…

Q: 5) Let Re(z) and Im(z) denote respectively the real parts of z, show that:- a) z+2 = 2 Re b) z-z =…

A: Introduction: Complex numbers are those that are expressed as a+ib, where a,b are real numbers and I…

Q: Let z, =1-1. z, =-2+4/, and z, =3-21.Find Im().

A: The given complex numbers are-  z1 = 1-iz2 = -2+4iz3 = 3-2iWe have to find ⇒ Imz1z2z3

Q: [1 2] If A = then show that |24|=4||| %3D 4 2

A: Introduction :We have given a 2*2 matrix A. We have asked to show that |2A| = 4|A|.

Q: 4.2. Let a, b E Z, where a 0 and b 0. Prove that if alb and bla, then a = b or a = -b. -b.

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

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Q: Let -1 2 2 A = 1 -1 0 and U =|-2, then determine if %3D 3 -1 2 U is in Nul A. U is in Col A (i) (ii)

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Q: Suppose that P ( A ) = 0.4,  P ( B ) = 0.5 and A , B are disjoint. Compute P ( A c ∪ B c ) .

A: From the provided information, P (A) = 0.4, P (B) = 0.5 The events A and B are disjoint.

Q: True or False   Consider the following model, Yi = β0 + β1Xi + ui,E[ui|Xi] = 0,i = 1,...,n…

A: Solution: As per the guidelines first three parts should be answered.

Q: Evaluate if a - 3, b - -2, c= 7, d = -1, and e = 0. 1. abc 10 -42 2. cde 14 3. ab + cd -13 4. cd+ ac…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: 1- Let z,=-5+11i and z3=2-21. Find in the form x+iy a) Re(1/2,) b) 1/ Re (z,) c) z,-z,? d) (z1/z2)

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Q: 4.2. Let a, b € Z, where a + 0 and b + 0. Prove that if alb and bla, then a = b or a = -b.

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Q: [1 2 3 3 9. Then the adjoint of A is given by: li 5 7] Let A =1 [-24 -91 24 -1 9. 11 -1 -11

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Q: Let A = 1 2 1 and v = If the entries of A and v belong to Z3, what is the third entry of Av? Answer:

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Q: 1 2 3 ) Assume A = 0 4 2 3 1 0 2 3 1 B= 1 2 5 2 3 1 Verify that AB ± BA :

A: Given matrices: A=123042310B=231125231

Q: 2. Let A € M, (R) be given. (a) If AA = 0n, prove that A = 0₁. Does this hold if A € M₂, (C)? (b)…

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Q: If X ∼ N (μX , σ2X) and Y ∼ N (μY , σ2Y ) are independent, then prove

A: X~Nμx,σ2x and Y~Nμy,σ2y are independant

Q: Let S= {1, 2, 3, Question 5. 4} and G = S,. Write all of the elements of GT and G(T) in each case.…

A: Given, S={1, 2, 3, 4} and G=S4 We have to write all the elements of GT and G(T) in each case. (a) T…

Q: Let a = (– 1, 5, 0) and b = (3,0, – 1). Find the component of b onto a.

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Q: linear algebra, 2.5 question 5

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Q: Suppose U = {x | 3 < x < 15, x € Z}, R= {x |5 < x < 8, x € Z}, and T={4,7,10, 13}. List the elements…

A: Given, set U=x|3≤x&lt;15, x∈Z consists a set of all integer numbers between 3 and 15 with including…

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.