O Consider the square matrix A=(a;)nen , where 「り、fi

Q: Construct a 3 x 3 triangular matrix A so that 1] the vector 2 is in Col A. 3]

A: We know every lower or upper traingular matrix is a triangular matrix.

Q: Complete the matrix A so that it is skew-Hermitian. i 2—6і - A = 1 9i Y = = 2

A: Given the matrix, A=0i2-6ix01yz9i The matrix A is said to be skew-Hermitian matrix if, A*=-A Where…

Q: A, 2x2 tipinde tekil(singüler) bir matris olmak üzere A.Ek(A) matrisi aşağıdakilerden hangisidir? A…

A: We're going to solve

Q: 27. Consider an n × m matrix A, a vector v in R", and a vector w in R". Show that (Av) · w = i · (A™…

A:

Q: if A is (m*n) matrix, prove 'rank(A)=n-dim(N(A))

A:

Q: let Amxn matrix , c scalar If cA=0, then Select one: a. c=0 and A=0 b. c=0 or A=0 C. C0 or A=0

A: WE have to check the meaning of cA=0.

Q: Consider the matrix A E RmXn with m >n and linearly independent columns. Also consider M = A(AT A)-'…

A:

Q: Assume that the matrix A is row equivalent to B. Without calculations, list rank A and dim Nul A.…

A:

Q: Given the matrix 2 2 2 A = 0 2 3 7 7 1 Find the |A| by transforming the matrix A to the triangular…

A:

Q: Answer considering the matrix with th e given vectors as its columns

A: Given: The given matrices are, Assume the linear combination as follows,

Q: For the matrix A in , use the Cayley ­Hamilton Theorem to compute A2, A3, and A4 by expressing each…

A: Given matrix is

Q: Let A be an m×n matrix. Explain why the followingare true. Any vector b ∈ Rm can be uniquely written…

A: For  matrix A, N(A) is the null space of A. R(A) is the column space of the matrix A and R(AT) is…

Q: Find a 2 x 2 matrix B + 0 and B + 1, such that AB = BA, where A How many such matri- 2 ces B are…

A: Given data: The matrix is given by "A". A=1221 Consider the matrix "B". B=abcd According to the…

Q: Let A be an n × n matrix and let D be an n × n diagonal matrix. (a) Show that D = (d11e1, d22e2, . .…

A: (a) The diagonal matrix D is of the form

Q: Assume that the matrix A is row equivalent to B. Without calculations, list rank A and dim Nul A.…

A:

Q: State Cayley-Hamilton theorem and prove this for following matrix [1 1 A 1 2 -1 %3D [5 8

A:

Q: Answer considering the matrix with th e given vectors as its columns

A:

Q: Let A be an n × n singular matrix. Then

A: if matrix A is singular that means its determined is zero.so at least one row of matrix A is…

Q: b) Prove: Let A be an m × n matrix, R" = NS(A) RS(A).

A: Given: Let A be an m×n matrix , Rn=NSA⊕RSA

Q: Prove that for any matrix A ∈ Mm×n(F), (R(LA∗))⊥= N(LA).

A: The objective is to prove that

Q: (b) Explain why in general, if u = [u uz] is a row of length 2, A = a1,1 a1,2 [@2,1 @2,2] we always…

A: Answer

Q: If the rows of an n X n matrix A are linearly inde­pendent as vectors in Rn, what is the rank of A?…

A:

Q: b) Prove: Let A be an m x n matrix, R" = NS(A) + RS(A). %3D

A: A be an m×n matrix, we have to prove that ℝn=NSA⊕RSA  …1.

Q: . Prove that (i) . =1, and (ii) ||, =\n (I is the Identity Matrix of order n).

A:

Q: 1. Let A = [a;j]4x5, B = [bij]4x5; C = [cij]5x2; D = [d:j]4x2, and E which of the following matrix…

A: Matrix addition: Let A be an m×n matrix and B be an also m×n matrix. A= {aij: 1≤i≤m ; 1≤j≤n} and B=…

Q: 5. Calculate the L and U matrix and proof that PA=LU. 10 -7 0 A = -3 26 5 -15

A: Firstly I find lower triangular matrix LL and an upper triangular matrix UU And the show that PA=…

Q: Find the dimension of the null space and the dimension of the column space of the -3 -2 7 7 [1 -27 2…

A: The given matrix, M=1-3-277-22-6-45147 we have to find dim(Nul(M)) and dim(col(M))

Q: I find the cooridinate matrix for A realtive to S=SA, Ag „Az, Au? where A= [2 0 and 1 1 00

A: The coordinates matrix for A is [a b c d]=aA1+bA2+cA3+dA4=A .see 2nd step.

Q: 2.4 Use this matrix N to rotate the point (0, 3) an angle of 180° anticlockwise around the point (1,…

A:

Q: Consider the ordered bases B = {1+x, 1 – x} and B' = {u1, U2} for P1(IR), and suppose that 2 Q = ( -…

A:

Q: Let A be the 2 x 3 matrix with entries aij = (i – 1)(j+ 1). Which of the following is the matrix A?

A: A be a 2×3 matrix. This means A2×3 . entries of matrix A are ai,j=(i-1)(j+1)

Q: Let A be the following matrix 7 7 7 3 3 7 Then for which column vector b, the equation Ax = bhas a…

A: Here given a matrix A of order 3×3. And also given a matrix equation Ax=b. We now find the b for…

Q: In exercises 8 to 13 , explain how your calculations justify your answer, and mention an appropriate…

A:

Q: ind a formula in terms of k for the entries of AK, where A is the diagonalizable matrix below. 4 -2…

A:

Q: Given the matrix 2 22 A = 0 2 3 7 7 1 Find the |A| by transforming the matrix A to the triangular…

A:

Q: Find a formula in terms of k for the entries of AK, where A is the Hermitian matrix below 13 4 9. 9.…

A: Here , A=-139-49+2i9-49-2i9-149 The characteristic equation of A is…

Q: Prove that (i) 7|, =1, and (ii) ||, =\n (I is the Identity Matrix of order n).

A:

Q: Explain why the columns of an nxn matrix A span R" when A is invertible. Choose the correct answer…

A:

Q: b) Consider the matrices C and D: C = D = -8 2 at 8.49.35 AM Calculate matrix 2C + 3D.

A:

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: Q3, Write any matrices A and B of order 3 × 3 and verify the results Let A and B be n n matrices,…

A:

Q: 1090 7, then A alla RA Have the same famk. 40. Prove: If a matrix A is not square, then either the…

A:

Q: Consider the ordered bases B = {1+x, 1 – x} and B' = {u1, u2} for P1(IR), and suppose that - 2 Q =…

A: Given that  β={1+x, 1-x} and β'={u1,u2} are order bases for P1(ℝ) and            Q=2-145    is the…

Q: Let A be nxn orthogonal matrix and v E R". Then ||Av||? = || ||?. %3D Select one: True O False

A:

Q: Assume that T and S are matrix of the same size. Prove or Disprove that (T + S) 2 is a symmetric,…

A: Given   T  and   S are matrix of same size. We have to prove if  T+S is symmetric, skew - symmetric…

Q: hatate the following triangle uith Q= 45° by the accemate diagram and I final matrix 12 C50,50)…

A:

Q: O Prove that if a matrix A satisfies A² = A, then I — 2A = (I — 2A)−¹.

A:

Q: 20. Can every vector in R* be written as a linear combination of the columns of the matrix B above?…

A:

Q: a) Prove that the matrix A = is diagonalizable if –4bc (a– d)². What happens when –4bc = (a– d)² ?

A: Given,         A= abcd

Q: Complete the matrix A so that it is Hermitian. 6 – 3i 1 A = -4 1 2 2 =

A: