A = [aij]nxn 0 ; i – j| = 1 ise 1; i– j| # 1 ise Which of the following is a matrix A written according to the condition given above? (i, j = 1, 2, .., n)

Q: a) If a 7 × 5 Matrix A has rank 2, find dim(Null A), dim (Row A) and rank AT

A: 1) Given  7×5 matrix  rank(A)=2 using rank nullity theorem we have rank A + null A= number of…

Q: Consider the 6 × 8 matrix 3 0 0 0 0 1 2 1 0 0 0 0 1 0 0 -3 4 -7 -9 A = 0 0 0 0 0 0 0 0 0 1 8 1 and…

A: The main objective is to answer the sub parts by using given matrix which is in reduced row echelon…

Q: 1) Construct the matrix A =(a;;) where 3x2 ) aj = i+j, if i = j,and Li-j, if itj %3D

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Q: 5: The Hessian matrix for f(x) = x³x3 + x2x3 at the point [1 2 3] is given by: [6 [18 0 31 0 671 20…

A: Let's solve.

Q: A is a square matrix that's n x n. A21=0 a) In-A is invertible, show why. b) B is invertible. Is B-A…

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Q: Which of the following is an elementary matrix, E, such that EA= B for 1 %3D 1 0 1 A = 2 2 and B = 1…

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Q: Let A and B be two matrices of size 4 x 4 such that det(A) 1. If B is a singular matrix then…

A:

Q: 3 91 Given a matrix A3 9 6 7] which of the elements aij follows the condition i=j. 9,9,1

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Q: 3. (a) Let In be the n x n identity matrix. What is det(-2In)? (b) If A is an n x n matrix and c ER…

A:

Q: Consider the Az 1 34 17 9 203 2 8 16 6 0 5 /

A: (a) We know that we can find the determinant of the matrix by expanding along any column or row.…

Q: (BH) Consider the following matrix in R5×5. * 0 0 0 0 0 0 0 0 0 * A = * * * where the *s are…

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Q: 2. If A1(t) and A2(t) are continuous in (a, b), and ¤(t) is a fundamental matrix of dX dX the…

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Q: 1 0 0 0 1 0 9. Suppose M Which matrix is M1? %3D 0 3 1 1 00 1 3 0 0 1 0. -3 0. 0. 1 O (1 0 0 0 1 0.…

A: Finding inverse of M

Q: 5. Compute the condition number K(A) of the following matrix 1 1+€ 1 1 1 A 1 1 1 1+€ What is k(A) as…

A: Conditional number is κ∞(A)=∥A∥∞·∥A-1∥∞.If matrix A is known to us so ∥A∥∞ is easy to find .First…

Q: Let n > 2 and let A be an n xn matrix. Prove that "det(adj A) = det(A)"-1."

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Q: **15. Suppose A is an m × n matrix and x e R" satisfies (AA)x = 0. Prove that Ax = 0. (Hint: What is…

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Q: If A is an nxn invertible matrix, then det(A-1) is equal to O det (A)-"det(adj(A)) O None of these…

A:

Q: A = (ai j )is a 3 × 3 matrix, develop the general ex-pression for det(A) by expanding(a) along the…

A: Given: Let A=aij be a 3×3 matrix.  To determine: The general expression for det(A) by expanding  a)…

Q: Which of the following matrices is a nilpotent matrix of degree 2. a a) where ab =-x². -x a where ab…

A: We have to select the nilpotent matrices of order 2 from the above list.

Q: 1. for how mony di fferent valves of x NOT Can the matrix T-x 2 3 Itx -I 3 be transformed by ERDS…

A:

Q: Let A and B be two matrices of size 4 x 4 such that det(A) = 3. If B is a singular matrix then…

A: We have given  det(A) = 3 If B is singular matrix  det(B)  = 0 detBT=det(B) =0 So,  det2A-2BT =0…

Q: Let be A, B, C,x. 5x5 matrixes such that A, B and C can be inverted such that AXB" – 151, = c-1…

A:

Q: compute e^At and e^-At of an identical matrix,I (1  0  0  1)

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Q: **32. Suppose A is an m x n matrix and x e R" satisfies (ATA)x = 0. Prove that Ax = 0. (Hint: What…

A: Here we use property of modular and dot product.

Q: 7. The rank of an identity matrix of order n is: А. п - 1 В. п C. n+1 D. 0

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Q: (a) The matrix ( (AB)-1 )T comes from (A-1 )T and (B-1 )T In what order?(b) If U is upper triangular…

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Q: If A is n x n matrix and (I- A)² = I- A then O a. AT = A %3D O b. AT A = I O c. AAT = I Od. A? = A

A: We have to solve given problem:

Q: Let A and B be two matrices of size 4 x 4 such that det(A) = 3. If B is a singular matrix then…

A: Let A and B be two matrices of size 4 x 4

Q: 1 4 What is a, if A = is a singular matrix ? %3D 2 a

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Q: Let Y-Nn(0,E)and let A be any nxn symmetric matrix. Show that m.g.f of Q=Y'AY is M(t) : det…

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Q: Let A and B be two matrices of size 4 x 4 such that det(A) = 3. %3D If B is a singular matrix then…

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Q: 2 1 1 1 2 1 0 0 1 Jse Cayley-Hamilton theorem to find A20 where the matrix A =

A: A=211121001A-λI = 2-λ1112-λ1001-λ…

Q: (iii). If A is ann x n invertible matrix, then show that det(A-1) det A

A: Given that A is an nxn invertible matrixWe know that A.A-1=I

Q: (1 4 6 8 0 2 3 4 0 0 3 8 \0 0 0 4 Is the matrix A = singular? Why? Find A- if it exists.

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Q: d the third column of A 'without computi 1 be found without computing the other om nted matrix (A…

A: The matrix is given as A=-2-3-2525431218. To determine the third column of A-1 without computing the…

Q: Let A = 0 1] 3 03 0 0 2 = If possible, construct P and D such that A don't need to compute P-¹).…

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Q: [1 Let A = 2 and V = |1]. What is the sum of the entries of the B = %3D 14 5 1 matrix VT (AT — (А -…

A: We have to find sum of entries of given expression.

Q: Let A = 3 0 -1 2 Compute the indicated matrix. (If this is not possible, enter DNE in any single…

A: Solve  for the A^3

Q: 1 a) Let A = 1 -1 %3D -1 1 (i) Compute the value of det(A). (ii) For what values of x will the…

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Q: Find the value of k such that matrix A is 2. k – 10 singular on Ik - 5 а. 1 С. 3 b. 2 d. 4 O D O B O…

A: Topic = matrices Correct option=D

Q: A be square matrix. I f A"= Onva for %3D n> 2. Then A= Onen

A: Suppose A be any square matrix of order n such that An=On×n     for n>2

Q: 4. Let Q E Rxn be an orthogonal matrix. Show that ||Qx||2= ||||2 for %3D any x E R".

A: Given that  Q∈ℝn×n be an orthogonal matrix.

Q: Let A = [a;;] be the n x n matrix defined by aji = k and a;; = 0 if i + j. Show that if B is any n x…

A: Given: A=aijn×n,     aii=k and aij=0 if i≠k. Let B be a square matrix of order 3 which can be…

Q: Suppose A is a 5 by 5 matrix with det(A) = 6 What is det(AT A)? Answer:

A: Given det(A) = 6

Q: Are there values of rand s for which i 0 0 r- 5 0 s-4 r+ 5 0 0 has rank 1 or 2? If so, find those…

A:

Q: -2 a wi a 8 Consider the matrix A = Oa. a = 4 O b. a = -4 OCAERI{- 4,4} Od. A is invertible for any…

A: Given:A=-2 aa8 Where  a∈ℝA is non-invertible matrixNon -invertible:     If the determinant of the…

Q: Let A be the n × n matrix given by Show that det (A) = (a - 1) n − 1(a + n - 1)

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Q: Consider the matrix 1 A = 1 1. Compute exp A. 2. Verify your calculation above using the identity…

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Q: 1 a) Let A = 1 -1 -1 1 (i) Compute the value of det(A). (ii) For what values of x will the matrix be…

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Q: [*:* а + 2 а (10) Find all a E R for which the matrix is singular. 1 а

A: Remark: A square matrix A of n is said to be singular if and only if det(A) = 0. i.e., Its…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.