True or False: Let A be an n × n matrix over C, then det(A¯) = det(A), where A¯ i,j = Ai,j . Here, z¯ = a − ib when z − a + ib, the complex conjugate of z.

Q: a Verify that det EA = (det E)(det A), where E is the elementary matrix shown and A =

A: E=1k01  A=abcd

Q: Show that no 2 x 2 matrices A and B exist that satisfy the matrix equation [1 0 0 1 АВ - ВА. %3D

A: In this question we have to prove that no 2×2 no matrices the given matrix equation.

Q: Let A be an 3 x 4 matrix. What must c and d be if we define the linear transfor- mation T: R → Rd by…

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: CD, where C and D are n x n matrices and C is invertible. Prove that the matrix product DC is…

A:

Q: Let A be a 5×5 matrix such that Ax​=b has a solution for every b in R5. Is it possible for Ax​=0 to…

A: Here, Ax=b has a solution for every b in R5

Q: Let A and B be nxn inversible matrix. Prove that AB is invertible and (AB)-1=  B-1A-1.

A: Let A and B be n x n invertible matrices, with inverses A-1 and B-1, respectively.

Q: Show that matrix A 5 1 0 5 cannot be diagonalized by using (λI-A)

A:

Q: (4) For the zero-one matrices A = and B = calculate %3D 0 0 1 1 (а) АЛВ (Ъ) АоВ (с) ВОВ

A: 4) Note:  AΛB = [aijΛbij] =[aijbij] , known as meet of A and B, only possible if matrix have same…

Q: Given that A, B, C are all square matrices of the same size, matrices A and C are both orthonormal,…

A:

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

A:

Q: Suppose A is a matrix such that A² + A = I, I is the identity matrix. Show that a) A must be square.…

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: Let A be an n xn matrix and B= A+ I, where I is the identity matrix, then it is possible for A and B…

A:

Q: Find inverse of matrix A by Gauss-Jordan me [2 -1 2

A: Here we have to find the inverse of the matrix by the Gauss-Jordan method.  we have,

Q: det(cA) = c det(A) Insert a number to sho

A: Given that  A is an n×n matrix and c is a scalar. Check whether detcA=cdetA is true or false.

Q: 2) If IAI = 3, where A is a 3x3 matrix, caleulate the folowing: 2a) det ( ZA) 26) det (A) 2c) det (…

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: If Aand B are invertible matrices of the same order, Then show that AB is invertible matrices.…

A: LHS   =  (AB)-1  RHS  =  B-1A-1 For    (AB)-1  =  B-1A-1 ,   RHS * inverse of LHS = i…

Q: Show that the matrix 2 1 A = 1 3 2 1 1 1 is invertible, but that A cannot be written as the product…

A: Solve the given problem.

Q: Show that the matrix A = singular. 1 -2 3 4 0 5 0 is 60

A:

Q: ?) A is an n x n matrix, such that 2A3 – 4A? + 6A – 21 = 0 (where I is the identity matrix and 0 is…

A:

Q: If A is a 2×2 matrix such that trace(A) = det(A) = 3, then %3D value of trace of (A-!) ?

A: Introduction: It is the sum of the diagonal elements of the matrix from upper left to lower right.…

Q: Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, [1 3 -2]…

A: A=13-223001-1

Q: Given Pauli matrices X,Y, Z ; show that X2 = Y2 = Z² = 1 (a) by using the matrix representation (b)…

A:

Q: If UT = U-1, then matrix U is an orthogonal matrix. %3D O True O False

A:

Q: (b) triangular with l's on its diagonal, and U is upper triangular. Use the results in (a) to obtain…

A:

Q: Suppose CA = I, (the nxn identity matrix). Show that the equation Ax = 0 has only the trivial…

A: Let A be m×n matrix then Rank(A) + Nullity(A) = number of columns of A Where Rank(A) is the…

Q: Let A be a 3 x 3 matrix such that 3a(1)- 2a(2)+7a(3)=0. Is A nonsingular? Explain.

A: A is singular matrix if rank is not full

Q: Suppose A-A, where A is the matrix. The det (A) is

A: Determinant of a null matrix is equal to zero.

Q: True or False? Suppose that A is any n x m or n xn matrix, then the matrix A'A will be the transpose…

A:

Q: Let A, B, C be invertible matrices of order 3x3. Show that if AB = AC , then B =C. %3D

A: Let A, B, C be invertible matrices of order 3×3. To show that if AB=AC, then B=C.

Q: Suppose AB = C, where A and C are upper triangular. (a) Find 2 × 2 nonzero matrices A, B, C, where B…

A: Answer

Q: If A and B are 3×3 invertible matrices, such that det(A)=2, det(B) =-2. Then det (ABA^T) = ???

A: To solve this problem, we use the standard result of matrix

Q: Let A and B be n x n matrices.  Suppose that AB = On where On is a zero matrix of size n x n, and A…

A:

Q: 1. For any 3x3 matrices A & B: Verify that (AB)" = B"A". %3D

A: By using the properties

Q: 2. Assume that A is a 3 × 3 matrix such that for 1 - (³).. ), j = 2 1 I 0 ;). it holds that Az = (a)…

A: Introduction: If the transpose of a square matrix with real numbers or elements equals the inverse…

Q: TRUE/FALSE Assume that all the given matrices are n × n. If A and B are row equivalent matrices,…

A: Given: All the given matrices are n × n. A and B are row equivalent matrices.

Q: Let A be an invertible, n x n matrix such that A² = A. a) Calculate det(A). b) If n = 3, what is A?…

A:

Q: Let A be 5x6 matrix. Knowing that Nullity (A) = 2. Then Rank(A) is equal to: * None of these O 2 O 1…

A: We will find the rank of A as following.

Q: Let A be a 6 × 5 matrix. What must a and b be in order to define T : R“ → Rº by T(x) = Ax? Ах?

A:

Q: Show that no 2 × 2 matrices A and B exist that satisfy the matrix equation

A:

Q: Let A be a nilpotent matrix of order n then A*n = 0 ) nxA = 0 A =nx1, l is Identity matrix

A: A be a nilpotent matrix of order n

Q: To find the multiplicative inverse of an invertible matrix A, we perform row operations on [A/ In]…

A: Given: To find the multiplicative inverse of an invertible matrix A, we perform row operations on…

Q: Show that it is impossible to find two real 2 x 2 matrices A and B such that AB - BA = dI where d…

A: Take A and B are arbitrary matrices and find AB-BA and analyse the diagonal elements

Q: Suppose that A is an n × n matrix satisfying the equation A4 + 2A2 − 3A − I = O , where I is the…

A:

Q: If A and B are invertible matrices and c is any scalar, then which of the following does not hold?

A: A and B are invertible matrices then  (AB) -1  = B-1 A-1

Q: a b Verify that det EA = (det E)(det A), where E is the elementary matrix shown and A =

A:

Q: [5 Let B =E dl: Is the matrix B orthogonally diagonalizable? If yes, find a diagonal matrix 2 0…

A:

Q: If A is any invertible n x n matrix, then rref( A) In. %3D True False

A: Invertible matrices, An n×n matrix A is invertible if there exists an n×n matrix B such that…