(A, B), ||A||, |B||, and d(A, B) for the matrices in M2,2 using the inner product (A, B) = 2a11b11 + a21b21 + a12b12 + 2a22b22 2 -5 -3 1 A = B = -1 1 0 (a) (A, B) (b) ||| (c) ||B||

Q: Find two 3x3 invertible matrices A and B, such that A+B is not invertible.

A:

Q: Suppose A is n x n invertible matrix ( AA-1 = I), then the first column of A-1 is orthogonal to the…

A:

Q: 5) Give an example of matrices D and F where DF is defined, but FD is not, and clearly explain why…

A:

Q: Let A = - 2     1    0                 1     0    1                2    -3    1        A is a…

A: trace is the sum of all diagonal elements of the matrix.

Q: A composite of matrices is said to be expanded if they are expressed as the sum or products of…

A:

Q: Suppose A. B and X are 'nxn matrices such that A and B are invertible, and Which one of the…

A:

Q: (0) Construct two non-zero 3x3 matrices A and B such that for A its rank is greater than its nullity…

A: two non-zero 3×3 matrices A and B such that for A its rank is greater than its nullityand for B…

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

A:

Q: VýB × VA

A:

Q: (4) Given a matrix X of independent variables, psudo-inverse X† is defined as (X"X)-'x" (a) If X is…

A: If a matrix is of order (mXn) then transpose of A is of order (nXm).

Q: A matrix A is similar to matrix B, if f invertible matrix P, B = P'AP. Prove is similar to B and B…

A: Given that: A is similar to B such that: B=P-1.AP.

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

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: Consider the matrix A given by 4. -5 3 6 -6 6 5 A = 9 3 -3 0 2 -4 Using elimination, find a lower…

A: LU decomposition of the matrix

Q: Let be A, B, C,x. 5x5 matrixes such that A, B and C can be inverted such that AXB" – 151, = c-1…

A:

Q: 3. Is the trace of the product of two square matrices equal to the product of these two matrices'…

A:

Q: Consider the multiplication AB is existing with the size (M × N) , where B is a matrix of size (L ×…

A: Consider the given information. The multiplication of two matrix is possible if and only if the…

Q: 4. If the product D = ABC of three square matrices is invertible, then A must be invertible (so are…

A: Given that the product D=ABC of three square matrices is invertible. Also given that A must be…

Q: DEMONSTRATE THAT A A-1= A-1A = I      FOR THE MATRIX BELOW     1 -1 2 2 -3 4 1 0 3

A: Given matrix A=1-122-34103 We have to  prove that AA-1=A-1A=I We know that A-1=AdjAA

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: 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: Let A, B, and C be invertible matrices. Then (4A-1B"C²)-1 is equal to c--(B")-1A equal to the above…

A:

Q: Verify by direct calculation that the matrix -2 -3 -1 A = 1 %3D 3. 3. satisfies the Cayley-Hamilton…

A: by cayley Hamilton theorem , " matrix satisfied its own characteristic equation " now to satisfied…

Q: Suppose A is a matrix that is 0 0 0 0 0 0 0 0 0 What is I-A

A:

Q: Suppose that A, B, C and D are n × n matrices satisfying the equation ABC = D. Show that if DA is…

A: Given:Suppose that A,B,C and D are n×n matrices ABC=DInvertible matrix:A square matix is invertible…

Q: What does it mean to say that A is a matrix with dimensionm  n?

A: A matrix is a rectangular array of elements arranged in rows and columns. The size of the matrix is…

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

A:

Q: (b) By replacing A with another matrix B different from A in only a single entry, define an inner…

A: To prove a function to be an inner product, we have to show it satisfies the following five…

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

A: By using the properties

Q: Suppose A +A+I-0 where A is a square matrix then A= A -A-I -2A A-I CS Scanned with CamScanner

A: Now we will find A-1 . Where I is identity matrix.

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: It's given that A,B are invertible matrices and A is also symmetric. If C =BA , D=AB and…

A:

Q: Using only 0's and l's, find the number n of possible 3 x 3 matrices in row canonical form.

A: We have to make all possible row echelon form ( row canonical matrices ) of 3×3 matrix with 0 and 1…

Q: Given a square matrix A of order n. If A is a lower triangular or upper triangular matrix, then…

A:

Q: Generalize the result by proving that, for any comfortable non-singular matrices A,B and C the…

A: Consider the given information. ABC-1=C-1B-1A-1 Multiply by pre and post C.…

Q: If A is a matrix in Rmxn with {()} -5 C(A) = span 2 %3D -2 what is m?

A: If A is a matrix in R^(m×n) then A is a linear transformation form n to m

Q: Verify that A = I when A =. l-8 -1 Use partitioned matrices to show that M² = I when 1 0 |-8 -1 0 0…

A:

Q: Suppose A and B are NONZERO matrices such that AB = [0]. Then there is no other matrix C such that…

A: Solution

Q: -0 의 B=[ 1 c=, 이1 1-0 1.where j--T, expres (a) Q3/B: If A = A.B, (b) B. C, (c) C.A and (d) A² in…

A:

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: a. Prove that (A'B*)-1= (A-B-1)* and B are 3 x 3 matrices and %3D b. If |A| = 4 |B|= -1 compute…

A: I have used the property of  transpose and inverse of product of two matrices and then show the…

Q: Suppose A is a matrix of order p × q and B is a matrix of order q × r, then illustrate the order of…

A:

Q: The aim of elimination steps in Gauss elimination method is to reduce the coefficient matrix to a)…

A: A matrix where the number of rows is equal to the number of columns is said to be a square matrix…

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: (b) Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, [1 3.…

A: Given :          A = 13-223001-1   To find the inverse of A. Also, to compute 3A-1.

Q: Find a 2×2 matrix A for which E1 = span [1      and      E2 = span [2                     2]…

A: