(a) Find an elementary matrix E such that EA = B; (b) Find an elementary matrix F such that F B = C; (c) Is C row equivalent to A ? Explain

Q: I. State whether or not the given matrix is (a) upper triangular, (b) lower triangular, (c)…

A: a) A matrix is upper triangular if all the elements below the main diagonal is zero Hence it is not…

Q: -1 Find all values of x such that the matrix 8 is not invertible.

A: A matrix is invertible, if the determinant of the matrix is not equal to 0 . Suppose a matrix B is…

Q: -2 2 1 Determine if the matrix A = -4 4 2 is diagonalizable. If so, find an invertible matrix P and…

A: Given matrix is A=−221−4421−10. First, we have to find the eigenvalues of A=−221−4421−10. The…

Q: (d) Let C be an nXn matrix. Explain why if the echelon form of C has at least one zero row, then C…

A: To prove, if matrix C has at least one zero row then the matrix is not invertible.

Q: 0 1 2 3 0 0 1 2 A = 0 0 0 1 12 - 0 0 0 0 A=[a] matrix can be expressed as

A:

Q: [A] Find all the minors and cofactors of the matrix 0. 2 1 A =| 3 -1 2 0 1] 4

A:

Q: An n x n matrix A is invertible if and only if it is row equivalent to I. 'n' O True O False

A:

Q: True or false? det(A) is a number, not a matrix.

A:

Q: eat) -1 = et) where A is a real matrix of class nxn . Error true

A: Given that, e^at-1=e^t where A is the real matrix of class n×n.

Q: ) Find a matrix A such that 3 A -3 1 1 EEE A =

A:

Q: b. If your answer in (a) is no, explain why it cannot be the case. Otherwise, obtain the…

A:

Q: e' Let M = be a fundamental matrix for the system X'= AX. Find the exponential 3e matrix eAt

A: Given :           M = et03ete2t is the fundamental matrix for the system X' = AX. To find :…

Q: -2 0 2 ) Let A = Find an invertible matrix U such that UA = R %3D 1 2 3 is in reduced row-echelon…

A: We will use elementary row operation to get U.

Q: -2 Find the matrix P such that P-'AP is diagonal matrix. -2 (c) Let A -2 3 -1 -1 3 6.

A:

Q: If A is an invertible matrix and (E-F)A=0. TS matrices E= F ? Justify your answer.

A: Given that, A is an invertible matrix. Also, E-FA=0. Multiply both sides of the above equation by A…

Q: The multiplicative identity matrix of order 3 is I =

A:

Q: If A is a skew-symmetric matrix of order 5 then adj(adj(A5«5)) = %3D

A:

Q: frequency. 2- Prove that matrix A is symmetric and matrix B is skew-symmetric 20 120 200 +34 10 150…

A:

Q: Given the matrix 1 0 1 -1 1

A:

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

A: Solving Part C only ..as you have already mentioned :-

Q: Shown below is a lower triangular matrix A. What will be the resulting matrix if A is rotated 90…

A: Rotate 90 degrees clockwise. Given information: The lower triangular matrix…

Q: (a) A matrix A is called an invertible matrix , if there exists a matrix B such that AB = BA= I.

A: A matrix A is invertible if there exists a matrix B such that AB = BA = In for some n, where In is…

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

A:

Q: (a) If the columns of annxn matrix A are linearly independent as vectors in R", what is the rank of…

A:

Q: a) ir(A - 1)1- ( -2) %3D Find the matrix A

A:

Q: The matrix A = is an orthogonal matrix. True O False

A:

Q: True or false? det(A) is defined only for a square matrix A.

A: True/False det(A) is defined only for a square matrix A

Q: 2. Let A be the matrix shown below A = [22] :) Find the matrix P that diagonalizes A.

A:

Q: For what values of λ ∈ R is the matrix invertible

A: The matrix A is invertible if and only if its determinant is non-zero.

Q: [2 1 0 4 1 0 1 0 0 1 6 1 Which of the matrices are not diagonalisable? Explain. Find the diagonal…

A:

Q: Use the invertible matrix theorem to determine the value(s) of A for which the matrix 4. A- 2. is…

A: This question can be solved using the concept of invertible matrix theorem which states that if the…

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: Find an LU factorization of the matrix A (with L unit lower triangular). -4 0 4 A= 8 3-5 8 12 13 ..…

A: Topic :- matrix algebra

Q: A lower triangular matrix of matrix A is c. L = Ex Ek1... E, E,. ... Ek1 E, d. L = E, E, a. L = E,…

A: A lower triangular matrix of matrix A is  .......

Q: Consider the matrix A of order 4 with a; = (-1)j if i <j and 0 otherwise. Which of the following is…

A: Given : A matrix A of order 4 with    To find the statement true for the matrix A.

Q: The symmetric matrix corresponding to the quadratic form X1 x2 = x} – 2x1x2 + 2x1x3 – 3x + 4x2x3 –…

A:

Q: Diagonalize the matrix A, if possible. That is, find an invertible matrix P and a diagonal matrix D…

A: We can use clever logic to eliminate wrong options.

Q: Let -1 1 A = -1 1 -1 -3 3 Find an upper triangular matrix which is orthogonally similar to A.

A: An upper triangular matrix is a triangular matrix with all elements equal to below the main…

Q: 1- the rank of the matrix A.

A:

Q: a For what values of a, b, and c is the matrix -a invertible?

A: For no values of a, b, c the given matrix is invertible.

Q: 1 0 1 3 0 2 6. Let A = and B = %3D 5 1 (a) Calculate the matrix Aª.

A: given matrix  A=1051 (a') to find A4 multiply the matrices using matrix multiplication. A4=A2·A2…

Q: Consider 1 A = 2 2 1 1 3 -1 -3 4 Convert A to an upper triangular matrix U by using Gaussian…

A: We have to convert the matrix A=121213-1-34 into an upper triangular matrix U by using Gaussian…

Q: Consider a matrix A, and let B= rref(A). %3D a. Is ker(A) necessarily equal to ker(B)? Explain. b.…

A: The matrix B=rrefA is the Reduced Roe Echelon form of the matrix A. The kernel of a matrix A is the…

Q: vector form, where A is row equivalent to the given matrix. 3 -3 7 1 -2 -9 5 1-4 5 0 1 2 -6 7. 9. [6…

A:

Q: If A is a matrix of order 3 x 6, Bis a matrix of order 6 x 4, then the product of order AB is ? 1) 6…

A: Given ,  A is a matrix of order 3 × 6 , B is a a matrix of order 6 × 4  Then ,  We have to find the…

Q: 13. Find the cofactor matrix and adjoint of matrix A A = 2 -2 1 3 1 3

A: The given matrix is A=3-2121313-2. The main objective is to find the cofactor matrix and adjoint of…

Q: a) Prove that the matrix A = is diagonalizable if –4bc (a– d)². What happens when –4bc = (a– d)² ?

A: Given,         A= abcd

Q: Diagonalize the matrix A, if possible. That is, find an invertible matrix P and a 0 0 diagonal…

A: