4) Given the matrix A= (! ), find all matrices B such that AB=BA. Check partic ular matrix B. your result on a

Q: If a 3 × 8 matrix A has rank 3, find dim Nul A, dim Row A, and rank AT.

A:

Q: FIND THE FUNDAMENTAL MATRIX AS WELL AS THE FUND AMENTAR MATRIX ø (6)= I %3D SATISEYING x' = 2 -5 -2

A: Fundamental matrix is formed with linearly independent solution sets of the system. These linearly…

Q: If A and B are nXn diagonalizable matrices, then A+B is also diagonalizable. True or False? Give an…

A:

Q: Find an LU factorization of the matrix A (with Lunit lower triangular). 4 -8 8 -4 A = 8 - 14 11 -5…

A:

Q: Explain why the matrix A + C does not exist.

A:

Q: If Q is an orthogonal matrix, prove that any matrix obtained by rearranging the rows of Q is also…

A: The matrix is said to be an orthogonal matrix if the product of a matrix and its transpose gives an…

Q: If A * I = A, and A is a 3x5 matrix, what are the dimensions of I? Show complete solution as proof.

A:

Q: Show that if A and B are two n × n matrices with the same diagonalizing matrix X, then AB = BA.

A:

Q: Let a = (a;) be an n-rowed square matrix and I12 be the matrix obtained by interchanging the first…

A: we have solved this question by using an example.

Q: If A and C arę nxn invertible matrices and B is an nxn matrix, then

A: By Theorem we can say that

Q: Suppose A is a symmetric nxn matrix and B is any nxm matrix Show that B'AB, B'B, and BB' are…

A:

Q: If A is a real n xn matrix, show that AA" and ATA are similar. (Hint. Start with an SVD for A.)

A:

Q: Let 2 -1 | -1 2 -1 -1 -1 -1 -1 –1 -1 2 -1 2 be the Eç Cartan matrix corresponding to the simple…

A:

Q: Find a 2x2 matrix that forms an angle of n/3 cadians with the matrix P -- (: 9) 2 0 0 2

A:

Q: 6. Show that if Q is an orthogonal matrix, then 1 0 %3D 0 Q is also an orthogonal matrix.

A: We have to show that HHt = I

Q: Suppose that A and B are orthogonal (n x ) matrices. Show that AB is an orthogonal matrix.

A:

Q: 11 A square matrix A is orthogonal if AA" = 1. What properties must be possessed by the columns of…

A: Given:

Q: Express the following matrix as a product of several elemen- tary matrices. 1 3 E 2 3 ||

A:

Q: Suppose that A is a square matrix with two identical columns. Can A be invertible? Suppose that A is…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: If Q is an orthogonal matrix, prove that any matrix obtained by rearranging the rows of Q is also…

A:

Q: 8.) If A is an mxn matrix, what are the largest possible value for its rank and the smallest…

A: As per the instruction, we will be answering only the first one. For (8), We have that A is an mxn…

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

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: If A is any 5 by 5 invertible matrix, then its column space is __ . Why?

A:

Q: Show that any matrix of size 3 by 3, can be written as the sum of two invertible matrices, that is,…

A:

Q: Show that if A and B are orthogonal matrices, then ABis an orthogonal matrix.

A: Given: A and B are orthogonal matrices. Therefore, AAT=I=ATA and BBT=I=BTB     . . .(1)

Q: If a matrix A has 2 linearly independent columns, then dimRow(A)=2. True O False

A: Please find the solution in the below step

Q: (4) Let A be a 3x3 matrix. If |4|= 2 , then |3.4|=,

A: Given that A be a 3*3 matrix and |A|=2. To find the value of |3A|

Q: 2. Determine the matrix X, such that:

A: Solution:-

Q: When a matrix is multiplied by a scalar k, then every entry of the matrix is multiplied by k.  True…

A: It is TRUE by definition which is given below.

Q: If A and B are orthogonal nxn matrices, then AB-1 is an orthogonal matrix. True False

A: here we must know that  1)  AA-1=A-1A =I2) ATT=A3) AI =IA =A

Q: Show that the matrix B′AB is symmetric or skew symmetric according as A is symmetric or skew…

A: Show that the matrix B′AB is symmetric or skew symmetric according as A is symmetric or skew…

Q: 4 Is the matrix a linear combination of the ma- 3 and 1 ? Justify your answer. trices

A: A matrix A can be expresses as a linear combination of two matrices B and C, if and only if there…

Q: 8.) Find the LU-factorization of the following matrix 1 2 2 2 3. 1.

A:

Q: O If A is possi ble value of dim Nul AT ? Please explain an 8x 5 matrix, what is

A:

Q: Suppose that Q is a matrix with the property Q−1 =QT . Show thatqij = Qij/det(Q)

A: Given: Q-1 = QT To Prove: qij = Qij/det(Q) Formula Used: If A is a square matrix, then its inverse…

Q: The multiplicative identity matrix of order 2 is I2 =_______.

A:

Q: If matrix A (mxn) has full rank, and I multiply it by its conjugate transpose A*. In other words,…

A: We will give a counter example that will prove this statement wrong.

Q: what is the Dim of a matrix, like if there is Matrix A, what is Dim(A)? Can i have example too?

A:

Q: Is the answer in #1 and #3 not in matrix form? how so?

A: Remember : eB represents coordinate matrix of e with respect to basis B. Which means if we consider…

Q: 29 What numbera in A-L makes A-QA@ possible (where Qis an orthognael matrix and A is an Zero or 1??

A: We shall solve this question by just using the definition of an orthogonal matrix. We know that a…

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: A matrix in which there is only one row and any number of columns is said to * .be matrix

A: Given:     Expression is ^-*33*425       In the prefix form of an expression, a binary operator…

Q: If a 6 × 3 matrix A has rank 3, find dim Nul A, dim Row A, and rank AT

A:

Q: Suppose A, B, and C are three non-zero square matrices such that AC = BC. Is it true that A = B? If…

A: Not true

Q: 1) Find a diagonal matrix A that satisfies A-2 20,

A: Here, we need to find a diagonal matrix A such that A-2=2004

Q: If A, B are two n x n orthogonal matrices, then AB is also an orthogonal matrix. True False

A: Give:  If A , B are two n×n orthogonal matrices. To check: product of matrices A and B are…