3) A = [3 Calculate the 10th power of the matrix with the Cayley-Hamilton Theorem.

Q: Suppose A = PRP–1, where P is orthogonal and R is upper triangular. Show that if A is symmetric,…

A: According to the given information suppose, It is required to show that if A is symmetric then R is…

Q: Find a (2x2) singular matrix A that maps (2, 4) into (3, 1).

A: Singular matrix mean its Determinant is equal to 'zero' .

Q: [3 Compute the natrix exponential e4t for the diagonal matrix A = !!

A:

Q: If the matrix A is positive symmetric definite, is BTAB also positive symmetric definite?

A: Let us define the function as, A¯=BTAB Then, A¯T=BTABT=BATBT=BABT   [A is symmetric]

Q: 32. Construct a nondiagonal 2 x 2 matrix that is diagonalizable but not invertible.

A: .

Q: 2. For the matrix 2 2 -1 B -3 3 find its Pseduoinverse Bt and the 2-norm ||B*||2.

A: Given : B=212-1-1-3-13 To find : pseudoinverse B+ and the 2-norm ∥B+∥2

Q: 2. Suppose A is a square matrix. Which matrix is not symmetric? O A+AT O AAT ОА-АТ O ATA

A: Note the following results if A and B are two matrices ABT=BTAT…

Q: .

A:

Q: If the Reduced echelon form of A-λI is the identity matrix then what is the eigenspace (Eλ)?

A: We need to find the eigenspace (Eλ) if the Reduced echelon form of A-λI is the identity matrix. Note…

Q: Is the matrix         1 0 0                               0 1 0                               0 0…

A:

Q: Consider the Az 1 34 17 9 203 2 8 16 6 0 5 /

A: (a) We know that we can find the determinant of the matrix by expanding along any column or row.…

Q: 2 Construct a 3 by 3 nonzero matrix A so that vector is a solution to Ax = 0 -

A:

Q: If A is 3 x 5 matrix with rank 1, then the number of special solutions to Ax = 0 is %3D O is

A: Since the rank of the matrix = 1. So the number of free variables = 5 - 1 = 4.

Q: Let C be a 5 x 7 matrix with a rank 4. (1) What is the dimension of the solution space of Ax 0?

A:

Q: .

A:

Q: If you know all 16 cofactors of a 4 by 4 invertible matrix A, how would you find A?

A: Given, an invertible square matrix A of order 4, and we know all the 16 cofactors of this matrix.…

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: 4. Prove that if A is a square matrix, then det(A™ A) = det(AA") %3D

A:

Q: 2. Suppose that A is a 64 × 17 matrix and that the rank of A is 11. What is the dimension of the…

A: The given matrix is A of size 64×17. Also the rank of A is 11. As we know that for any matrix of…

Q: If the null space of an 8 × 5 matrix A is 2-dimensional, what is the dimension of the row space of…

A:

Q: 5. Verify that the product of the non-singular matrix and its inverse from the previous problem is…

A: (5) Given matrix A=32−22 and its inverse is A−1=1102−223. We have to verify that AA−1=I2…

Q: A = (ai j )is a 3 × 3 matrix, develop the general ex-pression for det(A) by expanding(a) along the…

A: Given: Let A=aij be a 3×3 matrix.  To determine: The general expression for det(A) by expanding  a)…

Q: Let A be a m times nm×n matrix such that Ax​=b and Ax​=c each have a solution for some choice of b…

A: Let A be an m×n matrix such that Ax​=b and Ax​=c each have a solution for some choice of b and c in…

Q: Prove that the main diagonal of a skewsymmetric matrix consists entirely of zeros.

A:

Q: The Matrix B from 3 x 2 at b = 1- - is %3D 1. 2. 3.

A:

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: Suppose that A is a 5 x 5 matrix which has a null space of dimension 4. The rank of A is rank(A) =

A:

Q: 4. Suppose A is a nonsingular matrix with SVD A= UEV*.

A:

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: Use the method of Example 6 to compute the matrix A10, where 1 0 6 2 A =

A:

Q: In the LU decomposition of the matrix 4. if the diagonal elements of U are both 1, then 9. the lower…

A: Introduction :We have given a matrix , diagonal elements of the LU decomposition of this matrix are…

Q: 2 3 Show that the matrix A is singular. 4 6

A: Concept used: Singular matrix are the matrix that is not invertible. In other words the determinant…

Q: 4. A matrix A is similar to matrix B, if for some invertible matrix P, B = P'AP. Is B similar to A?

A:

Q: 2. Verify Calay-Hamilton theorem for the following matrix: (2 1 -1 A = (3 1 1 0 2

A: Solution:Given        A=21-1310102To findA-λI=0

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

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

Q: 1 Problem 2. For a nonsingular matrix A and nonzero scalar ß, show that (BA)- =A-. Problem 3. Prove…

A:

Q: If the null space of a 7 × 6 matrix  is 5-dimensional, what is the dimension of the column space of…

A:

Q: If the null space of a 5 × 6 matrix A is 4-dimensional, what is the dimension of the column space of…

A:

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: 1. Find the matrix P that projects points in the plane onto the line 5x - 2y = 0

A: As per honor code, we are entitled to solve only one question at a time so I am providing the same.…

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

A:

Q: 2. By using Hadamard matrices of order 2 and 4, construct a Hadamard matrix of order 8.

A: Given: Let us construct a Hadamard matrix of order 8 using the Hadamard matrices of orders 2 and 4.

Q: 10 choose a,b,c,d

A: 1. Option a is wrong as the columns of D are LI hence solution will be unique if exists. 2. Option b…

Q: Is it true that when an n*n matrix whose columns form a basis of R^n, then A is invertible?

A: We shall answer this in next step

Q: 2. Choose the rank of the matrix AT

A:

Q: Is it true that the sum of invertible n x n matrices is invertible?

A: Given: The statement is : Is it true that the sum of invertible n x n matrices is invertible? It is…

Q: 5. Show that the condition that the block matrices (8 ) m ( ) A 0 А С and B В can be matrices of the…

A: Given: The block matrices, A00B and AC0B.   To show: The given block matrices can be matrices of the…

Q: 3. Find LDU decomposition of the matrix [1 1 1] A = 2 4 3 3 7 6 (а) L 3D (b) D =, (c) U =,

A: Given: A=111243376To find: (a) L=?  (b) D=?   (c)  U=?