The rank and the nullity of A, respectively are [1 2 1 2 1 0 1 1 2 1 A 13 24 2 02242 0 0 0 0 0 "The Rank = "The Nullity= "

Q: 1 2 The rank of A =|0 1 is 2 4

A: We can find the rank as below.

Q: 2-j3 Given z = a + jb = Find a and b. 1+j

A: Given that                         z=a+jb=2-j31+j. Remember that here  j2=-1

Q: Determine z and y such that -3 31 x y 2 47 -1 %3D -1 -2 2. -3 2x+y 3

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Q: For which value of x is A = x= 4 1 -4 4 0 0 1 NOT invertible? -3 r

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Q: Let 1 0 -2 1 0 0 -1 -3 1 3 %3D -1 1 -1 1 3 0 -2 3 -4 Then nullity (A) O None 3 2 4 1.

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Q: For which value of x is A = x = 4 1 -4 4 0 -3 0 1 x NOT invertible?

A: The objective of this question is to find the value of x for which the given matrix A is not…

Q: [1 2 -3] Find det A A= 4 5 -9 0 1 0]

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Q: The rank and the nullity of A, respectively are 1 2 2 11 0 0 10 5 0 0 4 2 0 0 0 0 a. 2,2 b. 3,1 C.…

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Q: The rank and the nullity of A, respectively are 1 2 3 11 0 0 1 5 0 0 1 2 000 0 A = a. 1,3 b. 2,2 c.…

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Q: 1 1 2.- 2. Is b₁ = 2 in the null space of A=-1 L-3] 1 -1 1 1 -1? What about b₂ -1 1 ГО =6?

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Q: 10 -1 o -1 If A =: 1 1 8 in null(A)? is v = 1 v is in null(A). O v is not in null(A).

A: We find whether A is in null(A).

Q: . Let A, B = M₁ (F) where n is odd and the characteristic of F is not equal to two. Prove that if AB…

A: AB = -BA.  Take determinant on both sides, we get  det(AB) = det(-BA) = (-1)^n det(BA) = - det(BA) ,…

Q: 1-j 1 Evaluate a. b. 1+j 1+j

A: Given: 1-j1+j Now,  1-j1+j=1-j1+j×1-j1-j=1+j2-2j12-j2=1-1+2j1-(-1)=2j2=j Hence, 1-j1+j=j

Q: The rank and the nullity of A, respectively are 1 2 1 2 1 0 0 1 2 1 A= 000 1 2 0 0 2 4 2 0 00 4 8

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Q: Let i = (– 4, 4, 5) and i = (6, – 3, – 2). %3D • Hint

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Q: Let A= 1 0 1 0 0101 001 1 1100 What is the rank of A?

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Q: 6. Evaluate the det A where A = 1 0 -1 2 4 24 3 1 0 1 0 041 44

A: Given Matrix: A=14230144-10102041 To find: The determinant of the matrix. Concept used: i) There are…

Q: Let X₁, X₂,..., X be a r.s. from N(,0) and Y₁, Y₂...., be another independent r.s. from m…

A: Solution

Q: 1. A service station has both self-service and full-service islands. On each island, there is a…

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

Q: -1 2 1 Let A Compute AAT and AT A. 1 0 1 1 -1

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Q: هدى الدالة 2x - = y هو. %3D

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Q: 2 3 2 3 2 3 Let G= S3 and H={(; 3 2 Then the number of disjoint cosets in G/H is H. 6 O 3 2 O

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Q: The coefficient of correlation of the two variables a) is negative. b) is positive. c) should have…

A: The given plot shows the scatterplot.

Q: -1 1 2 A 3 3 4 det A 0 0 -2 0 0 2 4 B = -5 6. 1 5 3 3 det B: -1 0 0 0 3 0 0 C = 2 0 0 4 0 0 0 0 -2…

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Q: 3. Prove that if a E Z then the only positive divisor of both a and a + 1 is 1.

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Q: -1 1 0 -1 If A = is v = 1 in null(A)? 4 1 1 -1 O v is in null(A). O v is not in null(A).

A: Given that: A=10-1111  and v=-14-1

Q: Find gcd(2,3+5i) in Z[i]

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Q: Given A=[1−5  1-3] compute 5A

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Q: In a random sample of n pairs of values of X and Y,(xi, yj) occurs fij times for i = 1, 2, ... ,r…

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Q: The div A at p(1,1,2) for A is .... Å = x²y i + 2 x z j + 4 - z² y k - 3 ( 3 зі зј о

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Q: -3 and y = 2 0 Let x = ||x - y||₁ ||x - yl|oo = ||x - y||2₂ = 3. Compute

A: Given : x=-5-32    , y=330

Q: A = 1 - 2 3 k 0 1 2 -k -4

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Q: 103 Let = 2+j"8 and z, = 4+ j06. Show that a. + =2 = =, +z2 b. 1- 2 = =-2 с. d.

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Q: ion # 19 b+c=8, ab+ bc +bc+ ca-17, abc =10, then the value of (2-0(2-6)(2-)is:

A: Given: If a+b+c=8 ab+bc+bc+ca=17   abc=10  To find: (2+a)(2+b)(2+c)

Q: التاريخ | | 3 1 오구니 -2 M= -3 * A = M+N *B=A-M *E = A*B = F = Transpse E G 7 4 6 9 2 Multiply F by 3…

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Q: If lx - -3, flye - 2,0-2, a²-5 and oxy - 1, find the covariance between U - X + 4Y and V = 3X-Y. 4…

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