Let a be a real number, and consider the matrix a 2 1 1 6 3 A =

Q: For matrix A, B if A – B = O, where O is a null matrix then * A = B B = 0 A = 0

A:

Q: If A is a square matrix such that A2 = A, then (I-A)+A is equal to (A) (В) (C) I- A (D) I+ A

A: A is a square matrix such that: A2=A Now: (I-A)3 + A=(I-A)2(I-A)+A =(I2-2AI+A2)(I-A)+A = (I-2A + A)…

Q: Let A be an m × n matrix. ☎ € Rm. The solution set of Ax is the same as the solution set of AT Añ =…

A: We need to answer if the given statement is True or False

Q: Find the matrix A such that 1 0 A -2 -3 -1 3 -1 a b Hint: Let A = c d C A =

A: Given a matrix A -             We have to find-

Q: Find a matrix B such that AB = I, where 4 1 1 0 A = and I = -4 4 1 a b Hint: Let B c d B =

A:

Q: Find a matrix B such that AB = I, where 6 1 A = 1 0 0 1 and I = -6 6 a b Hint: Let B =c d

A:

Q: Let A and write A as the sum of a symmetric and skew-symmetric matrix. The skew-symmetric matrix is…

A:

Q: Use the matrix P to show that the matrices A and A′ are similar.

A:

Q: In Exercise, find the singular values of the given matrix.

A: Given matrix will be as:- A = 1100   and   AT= 1010 Now,  ATA = 11001010 = 1+1000=2000 To Find the…

Q: Let a matrix '2 -2 1 A 2 3 1 1 -2 - 2 2 Show that A"A = I and deduce that AT = A-1.

A:

Q: (2) Consider the matrix -[: ] A = Find the unique x, y E R, such that A? = xA – yI (where I…

A:

Q: Let A and B be 3 × 3 matrices such that A 3 = B 6|. The matrix C = A – 2B is invertibl A) True False

A:

Q: Give an example of a nonzero 2 X 2 matrix A such that A2=O

A:

Q: Determine whether the given matrix A is diagonalizable. If so, find a matrix P that diagonalizes A…

A: Given matrix A=01-12 and A=200121-101To find: A matrix P that diagonalizes A and a diagonal matrix…

Q: Let [ 2 A = 6 -1 and B = %3D Find an elementary matrix E such that EA=B.

A: An elementary matrix is one which differs from the identity matrix by one elementary row operation.

Q: Prove that for any square matrix A, ||A||3 E ||A* A||2.

A: For any square matrix A Required to prove A22 <=A*A Let, us consider the matrix, A=2314

Q: Find a 3 x 3 matrix A such that 1 -5 A 3 A 1 -3 and -2 A 4 1 -5 A = 3. ||

A:

Q: Let A and B be 3 x 3 matrices such that A 3 = B 6 l10! The matrix C = A – 2B is invertible. %3D [5.

A:

Q: Let A and B be square matrices of order 2 such that |B| = 4 .What is ( AB) '

A: To see 2nd step

Q: Find the SVD of the matrix: 1 2 34 A = 0 0 0 0

A:

Q: Find all a,ß>0 so that the matrix 3 2 B [4]= a 5 B 2 1 a is strictly diagonally dominant.

A:

Q: Express A and A- as a product of elementary matrices. [1 0 51 A = 0 16 li 0 3

A:

Q: If A is a square matrix such that A =1, then A'is equal

A: Given, A is a square matrix such that A2=I.

Q: Let A be a square matrix such that A = 0. Show that 4 : (I – A)-1 = I+ A+ A? + A³. Here I is the…

A:

Q: Show that ∣A∣ = ∣AT∣ for the matrix below.

A: Now the transpose is,

Q: Let A be a square, invertible matrix and let A' be its transpose. Which of the following statements…

A: Solution

Q: Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, A = [6…

A: We have to find the inverse

Q: In Exercise, find the singular values of the given matrix.

A: We have the given matrix A as A=34 Now, transpose of matrix A is calculated as AT=34 Now, the value…

Q: Let A be a 2 x 2 matrix a If ad – bc + 0, then A-1 ad-be ad-be ad-e ad-be. such that [1 AA-1 = A-'A…

A:

Q: Let A be a 2 x 2 matrix. If det (A) # 0, then det (adj A) = det (A).

A:

Q: Show that if A is a square matrix that satisfies the equation A2 - 2A + I = O, then A-1 = 2I - A.

A: Given that,                    A2-2A+I=0

Q: Let A and B be square matrices of order 3 such that |A-| = x + 7 with x + -7 and |A * A" | = . What…

A: A and B are square matrices. Therefore, det(AB)=det(A).det(B) det(A)=det((A)T) We will use these…

Q: In Exercise, find the singular values of the given matrix.

A: Consider  A=2102. Now ATA=20122102=2223

Q: Use the Cayley-Hamilton theorem to find A1, A°, and A“ for the given matrix A. 1 5 1 A = 0 2 1 0 0 2

A:

Q: Let A be the matrix 4 2 7 6 Find p(A). p(x) = x – 2x + 4 i i p(A) =

A:

Q: Find all a > 0 and B>0 so that the matrix 3 2 B A A =| a 5 B 1 is strictly diagonally dominant.

A: The given matrix,A=32βα5β21α

Q: Let A and B be 3 x 3 matrices such that A 3 = B 6 l10. The matrix C = A – 2B is invertible. [5. (A)…

A:

Q: Let A be a nonsingular 4 x 4 matrix such that |A-1| = -2, then AT.adj(A-}) Select one: O True O…

A:

Q: Find the value of k such that matrix A is singular: (1 2 A = | 5 -1 2 6. k.

A: Singular Matrix: A square matrix that is not invertible is called singular or degenerate i.e., it is…

Q: Let A and B be square matrices of order 4 such that ∣A∣ = 4 and ∣B∣ = 2. Find (a) ∣BA∣, (b) ∣B2∣,…

A: Let A and B be square matrices of order 4 such that ∣A∣ = 4 and ∣B∣ = 2. We need to Find (a) ∣BA∣,…

Q: Find an invertible matrix P and a diagonal matrix D such that P AP=D. 4 0 0 18 2 0-36 0 0-2 -4 %3D 6…

A: Find the invertible matrix P and diagonal matrix D such that P-1AP=DA=400-41820-3600-20600-6

Q: .

A:

Q: Let A = (a;;)ij be an m x n matrix of real numbers, and let f : R" Rm be defined by 0-0 x2 x2 f = A

A: To find the derivative of f given: matrix A which has m rows and n columns  also the function f…

Q: Enter a 3 x 3 symmetric matrix A that has entries a11 = 1, a22 = 5, a33 = 4, a12 = 3, a13 = 2, and =…

A: Given A is 3×3 Symmetric matrix with entries a11=1 , a22=5 , a33=4 , a12=3a13=2 and a32=0.We know…

Q: Let A be the matrix 5 3 2 Find p(A). p(x) = x³ – 2x + 4 p(A) =

A: Given: A=5312 and p(x)=x3-2x+4.

Q: O Let A be an m x n matrix, and let B be the result of performing a single elementary row operation…

A:

Q: Let A be an n × n matrix and c a real number. Show that if cA = O , then c = 0 or A = O .

A: Given: A be an n × n matrix and c be a real number. To prove that: if cA=0 , then c=0 or A=0.

Q: Consider the matrix B given by 0 0 0 B = 1 0 0 0 1 0 Show that B3 = 0. Also, compute for the product…

A:

Q: 1. Identify the two-by-two matrix with matrix elements a;j = i – j. O (1 (금) ㅇ(9) (오 ㅇ (? )

A:

Q: a Let A = b be 2 x 2 matrix such that d 3A' +2 Find A. 1

A: