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

Q: Determine whether the matrix is orthogonal. An invertible square matrix A is orthogonal when A−1 =…

A:

Q: Express the invertible matrix (1 2 1 10 1 1 2) 1 as a product of elementary matrices.

A:

Q: Let A and B be n × n nonsingular matrices. Find nonsin- gular matrices P and Q so that PAQ = B.

A: Given that A and B  are n×n non singular matrices. An n×n matrix A is non singular only if A is…

Q: Let A be a 3 x 3 matrix such that A3 - 6A² + 4A – 31, = 0. Then, A is invertible and 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: Is it possible for A3 to be an identity matrix without A beinginvertible? Explain.

A: To explain:It is possible for A3 to be an identity matrix without A being invertible.By definition

Q: Let A and B be invertible 5-square matrices such that A| = 4 and B = 2. Then |2A. B 2 %3D

A:

Q: Find x such that the matrix is singular. 4-[94] A

A:

Q: Let A and B be square matrices of order n satisfying Ax = Bx for all x in Rn. (a) Find the rank and…

A:

Q: Find x such that the matrix is singular. 4 X A -2-6 X3D

A: Given Matrix is, A=4x-2-6 we know that, A matrix is said to be singular if it's determinant is zero.…

Q: - |A°| |B°| • |4°|

A:

Q: Let A and B be two square matrices. Assume that both A and B are invertible. Show that BA is…

A: Note that--- If determinant of a matrix is non-zero then the matrix is said to be invertible and if…

Q: Let A and B be two skew-symmetric matrices of the same size. Show that AB+BA is symmetric.

A: Given that: Let A and B be two skew-symmetric matrices of the same size. To show: AB+BA is…

Q: Let A be a matrix 4 0 0 0 0 4 0 0 0 0 2 0 1 0 0 2 Determine if A is diagonalizable, and if…

A: Solving the above matrix problem using row operations

Q: Let A and B be two square Matrices of the same Size such that A is not invertible (B may or not be…

A:

Q: (a) Let A, B be n × n symmetric matrices such that XTAX = X™BX for all column vectors X e R". Show…

A:

Q: 6. Find the distance between the matrices A and B, p(A, B), using the ||- ||2 for the matrix -[:] -1…

A:

Q: Suppose A and B are orthogonal matrices. Show that A", A-1, AB are also orthogonal.

A: we have given A and B are orthogonal matrices.  We have to show that the following

Q: * Find the Matrix B from order 2 x 4 , Its elements are written in the form by = i + ()

A: Here we find matrix B of order 2×4

Q: Г1 3 2 5 1 [3 4 2

A:

Q: A = 2 - 4 4 -2 6-9 7 -3 -1 -10 18 -7

A: Sol

Q: Prove the Frobenius theorem in the case where A is a 2 ×2 matrix.

A: This theorem is not valid for order less than 3

Q: Let A and B be two matrices of size 3 x 3 such that det(A) = -2 and det(B) = 3. Then det(2A-'B") =…

A:

Q: Find two 2 × 2 matrices A such that A2 = I.

A:

Q: Let A and B be n x n matrices, and let c be a scalar. Prove that(A + cB )* =A* + cB*.

A: Consider the given relation, A+cB*=A*+cB* The Conjugate transpose of n×n matrix A is n×n matrix A*…

Q: Find nonzero 2 × 2 matrices A and B such that AB = O.

A: Consider

Q: Prove det(A) = det(A'), for an upper triangular matrix A.

A:

Q: Define what it means for a function Q : R" R to be a quadratic form. Furthermore, explain how we…

A: The quadratic form is one of the most important parts of linear algebra. Quadratic means degree two.…

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: Let r1, .. r,be vectors in R", and let Q be an m xn matrix. Write the matrix Qr, Qr, as a product of…

A: Given:Let r1.......rp be vectors in ℝnLet Q be an m×n matrix Qr1.......QrpR=r1.......rpQ=Q…

Q: -) Let A, B be nx n symmetric matrices such that XTAX = X™BX for all %3D column vectors X e R". Show…

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Let B = and B' = Find the change of base matrix from B' to B and from B to B'

A:

Q: Explain transpose AT of the m x n matrix A?

A:

Q: A is a reversible matrix of nXn. Show that |adjA|=|A|r1

A: As we know that the inverse of a matrix A is : A-1=adj(A)|A|

Q: Let A, B and A+B be invertible matrices of order n. Show that also A +B¯! is nonsingular and that =…

A:

Q: Let x and y be square matrices of order n a. Show that if x and y are skew symmetric, then x + y is…

A:

Q: Find 2x2 invertible matrices A and B such that A + B not equal to 0 and A + B is not invertible.

A: Wee need to find matrix A and B and do their addition and find invertible

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: Let A be a lower triangular n x n matrix with nonzero entries on the diagonal. Show that A is…

A: Consider A be a lower triangular matrix with non-zero entries on the diagonal.

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: Find two different 2 x 2 matrices A such that 1 0 A? =

A: Given: A2=1001

Q: let  A and  B be  square  matrices of order n  such that  Ax=Bx  and x belongs to Rn  then   find…

A: Ax = Bx implies  Ax - Bx = O So, (A - B)x = O where x belongs to Rn  So, x belongs to the null space…

Q: Let A and B be square matrices of order 2 such thatA=-7 and B=4.What is (ABY"| %3D %3D

A:

Q: Let Q be an orthogonal matrix such that QA makes sense.                          Show that (QA)+ =…

A: Given, A be a matrix and Q be an orthogonal matrix such that QA makes sense. We have to use product…

Q: Let A be a mxn matrix that n > m (a) Explain why A = 0 has at least a non-trivial solution. %3D

A: (a) Given that A is an m×n matrix. The objective is to explain why Ax=0has non trivial solution.…

Q: 2. Find the matrices P and D for an orthogonal diagonalization A=PDPT for 3 0 0 A=

A: First find eigenvalues eigenvactors corresponding to eigenvalues then we get matrices P and D.

Q: Show that there are no 2 X 2 matrices A and B such that AB - BA = I2

A: Given- There are 2×2 matrices A and B. To disprove- That AB-BA=I2