e) Let A be an n x n matrix. If det(A – AIn) = 0 for some ) e R, then det(A² – X²In) 70.

Q: Given that G is a 1 × 6 matrix and H is a 6 × 1 matrix, a. Is GH defined? If so, what is the order…

A: Given that G is a 1 × 6 matrix and H is a 6 × 1 matrix,a. Is GH defined? If so, what is the order of…

Q: Let A be an m × n matrix. Show that if x ∈ N(ATA), then Ax is in both R(A) and N(AT ).

A:

Q: A matrix Q ∈Mn×n(R) is called orthogonal if QQt= I. Prove that if Q is orthogonal, then det(Q) = ±1.

A: The determinant of the product of the matrices is the product of the determinant of the matrices.

Q: The mist Consider ann x m matrix A. Find dim(im(A)) + dim(ker(A")), in terms of m and n.

A: Please check step 2 for the solution.!

Q: If A is an n×n matrix with Col A​ = Rn​, how many solutions will there be to Ax​=b​, for any b in…

A:

Q: An n x n matrix A is orthogonal if AA" = I. If A is orthogonal show that det(A) = ±1.

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Suppose T: R° → Rª is defined by T(x) Mx and M is a 24 x 19 matrix. Then %3D a = b =

A: If T: from Rb to Ra then M is always a×b matrix.

Q: where En is a k-dimensional vector, A e Ckxk is a constant matrix, and B : Z+ Ckxk is a matrix…

A: Given,      tn+1-t¯=∑i=01αi(tn-i-t¯)+∑i=01βi(zn-i-z¯)…

Q: Given the bases B={U , u2} and B'={u'1, u'2} for R2, where and u'1= u'2 = The transition matrix Pa-g…

A: The given bases are B={u1,u2} and B={u1',u2'} where u1=10  ,u1=01   and  u1'=-10  ,u1'=01 . To find…

Q: Is it true or false? If A is nxn matrix, c is scalar, then cA |=c | A| Birini seçin:

A:

Q: Given a 3x matrix in terms of scalar c and that det (A)=8, find the valuddof G if -1 1c-2 C+7 3. 2.

A:

Q: 9. . Suppose that A = PDP¯' and B = 31 + 2A + A². 5 Let D a Find a diagonal matrix D1 such that B =…

A:

Q: 2). For what values of t, the following matrix will be singular (7%4) t - 1 1 -2 t + 2 -1 t+1

A:

Q: 11. Let A be an m x n matrix and let x, y e R". Prove that if Ax = 0 and y = ATb for some b e R",…

A:

Q: If A is a skew-symmetric n X n matrix and n is odd, prove that det A = 0.

A: Since A is a skew-symmetric matrix we have,  AT=-A where AT is the transpose of matrix A. Then we…

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: If A is an n × n matrix, show that (Ak )T = (AT )k for any positive integer k.

A: Matrix: We will solve it by the method of induction:(Ak)T=(AT)k case 1: k=1case 2: k=ncase 3: k=n+1

Q: Let A be an nxn matrix. If A-= det A adj A is computed, what should AA be equal to in order to…

A: Using the given matrix equation we need to find the value of AA-1 .

Q: (i) Use the properties of trace to argue that tr(AʼA) = tr(AA') for any n × m matrix A. [2 0 (ii)…

A:

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

A: Now the transpose is,

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…

A:

Q: Find a 3 × 2 matrix T, such that TT' = A, where 4 A = |4 3 3 5

A: Given: To find a 3 x 2 matrix T, such that TT' = A,  A = 540453035

Q: (4) Given matrix A = 3 and that h(T) = T² – 2T – 7, find h(T).

A: see 2nd step.

Q: (d) Suppose A is a 2 × 2 matrix such that for all x, y E R?, (Ax) · (Ay) = x · y Must it be true…

A: This is the problem of linear transformation.

Q: Let B be an n X n matr ix and let E be an n X n elementary matrix. Then det(EB) = (det E)(det B)

A:

Q: Let A be the following matrix 3 7 4 8 4 7 1 2 4, After diagonalization, P and D are found such that…

A:

Q: Given the bases B={u , U2} and B' ={u'1, u'2} for R2, where and u'1= u' 2 U2 from B to B' is: The…

A:

Q: For a matrix A having JA| = 0, which of the following are true? * O A- exists with |A¬' |= 0| O A-…

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: メ-E to to L-E 2-E to to to d-E put K-E =U E= d-fX

A: The solution to the given question is explained below.

Q: (4) Given matrix A = ( ), and that h(T) = T² – 2T – 7, find h(T).

A:

Q: (4) Given matrix A = G ). and that h(T) = T² – 2T – 7, find h(T).

A:

Q: If a is skew symmetric nxn matrix and n is odd,prove that det A = 0.

A: Consider a skew symmetric n x n matrix A where n is odd. Here the objective is to prove that det(A)…

Q: Let A E Mn(C) denote the n x n matrix with all entries equal to 1. Show that A is positive…

A: Let A belongs to  Mn (C) denote the n x n matrix with all entries equal to 1. Show that A is…

Q: (4) Given matrix A = and that h(T) = T² – 2T – 7, find h(T). 5

A: i have answered this question in step 2.

Q: Given C and D are matrixes, and their products CD and DC exist, what can we tell about their…

A: Matrix multiplication is the process of multiplying two matrices using dot product. Dimension of a…

Q: •(b) A = B:

A: Given,        A=-1201,   B=1-201

Q: Suppose A is a 2 x 2 matrix such that for all x, y E R², (Ax) · (Ay) = x ·y Must it be true that A…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: if A is (m*n) matrix, prove 'rank(AB) < max(rank(A), rank(B))' only A: (m*n), B : (n*k)

A:

Q: Let B be a Sx5 matrix and Caa): (a-1)(X-メーい(メ) Than the rann of 21-B is? A)S B) 4 c) 3 D) can't…

A: Rank of any matrix is equal to number of non zero rows of matrix when it is in row reduced echelon…

Q: (4) Given matrix A and that h(T) = T? – 2T – 7, find h(T). =

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: Given the bases B={u, U2} and B' ={u'ı, u'2} for R2, where , U2 and u'1= u'2 The transition matrix…

A:

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: W is a 120 x 60 weight matrix, What are the dimensions of dW? According to the principle of…

A: Given that W is a 120×60 weight matrix. We have to find the dimension of dW Since, we know that…

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

A: