-2 6. What is the diagonal matrix Find an orthogonal matrix Q that diagonalizes A = 6. 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: 1. By hand, find the QR factorization of the matrix

A: QR factorization means A = QR Where, Q is an orthogonal matrix with orthogonal columns and R is an…

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: Find an orthogonal matrix Q and a diagonal matrix D

A: Follow the procedure given below.

Q: 6.* Let C be a nonsingular matrix with 3 rows and 2 columns. Explain why C has a left inverse.

A:

Q: e/ By three ways Show that B= %3D isorthogunal matrix

A:

Q: 4. Find the cofactor matrix for the matrix. 5 9 1 8 5 6 4

A:

Q: orthogonal matrix P and a diagonal matrix D diagonalising  A = [5 2; 2 8]

A:

Q: |adjA| = |A]"=1 n-1

A:

Q: 1. Given the linear combination below, try to create a corresponding matrix representing it. Use…

A: The representation of the above equation in matrix form is in the image below.

Q: Which of the following is the LU-factorization of the matrix a) 1 b) 0 1 1 c) d)

A:

Q: 6. (a) Find the matrix A so that AB=C, where C1 C2 C3 b, b, bz 2 B= b, b2 b3 & C= C1 C2 C3) а, а аз…

A: AB=C

Q: which of the following is the cofactor A13 of matrix?

A: Simply omit that raw and column whose co-factor matrix required and write rest all elements in same…

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: 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: Find diagonal matrix D is similar with A a A =[? -5 And make sure can transtor diagomalizablewith

A:

Q: Let A be an n × n matrix and let B = A + I. Is it possible for A and B to be similar? Explain.

A:

Q: Let A be a 4 × 4 real symmetric matrix witheigenvaluesλ1 = 1, λ2 = λ3 = λ4 = 0 What type of matrix…

A: Given, A is a 4×4 real symmetric matrix with eigenvalues 1, 0, 0, 0. Now we have to find what is the…

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: -2 2 Let A = Find a matrix P that orthogonally diagonalizes A. Then, verify that 1 the equation P™…

A:

Q: b) If C is an orthogonal matrix and D = C + C-1 show that D is a symmetric matrix.

A: We have to show D is symmetric.

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: ?) A is an n x n matrix, such that 2A3 – 4A? + 6A – 21 = 0 (where I is the identity matrix and 0 is…

A:

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: Identify a matrix P that diagonalizes 2 6 A = a. 1 P = - 2 Ob. P = -1 0 0 2 Oc. P = 01 1 2 O d. -2 P…

A: Solution

Q: If A is an m × n matrix of rank r, what are the dimensions of N(A) and N(AT )? Explain.

A:

Q: 3 Given that matrix A = (, and matrix B = 1. From the matrix above, 3 Determine the values of x and…

A: The given matrices A=35-10 and B=x0y1

Q: Consider the following matrix: -31 A = -3 -4 9. 1 -2 (a) Verify that A is diagonalizable. (b) Find…

A: Since it is multiple questions with multipart, as per our company guidelines we have to solve the…

Q: erse of the given matrix

A:

Q: If xER" is a column vector (i.e. an n ×1 matrix), then In-2xx' is always a symmetric matrix. True…

A: Consider the given column matrix as x=x1x2⋮⋮xn-1xn, x∈Rn. Compute the transpose of the matrix x as…

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

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

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: 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: (e) Suppose we just had the matrix A, but not the expression that was used to generate it. He we…

A: Suppose we just had the matrix A but not the expression that was used to generate it.

Q: [ -2 2 Let A = 2 i Find a matrix P that orthogonally diagonalizes A. Then, verify that 1 the…

A: Given that,A=-2221The matrix P that orthogonally diagonalizes A is determined as shown below.

Q: 3. Consider the following matrix: -31 A = |-3 -4 -1 -2 3 2 9. (a) Verify that A is diagonalizable.…

A:

Q: Find a matrix C such that A = CB for the matrices 1 4 5] A = |-2 0 1 3 1 0 -4 0 2] B= | 1 4 5 5 5…

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: 3. Consider 3x3 matrix A the 1 A て 1. レ Colculate the adjoint matrix

A:

Q: 7. ). Find all a and 3 > 0 so that the matrix B : 23 6 2 is %3D В 2 diagonally dominant; 12G

A: For a matrix is to be diagonally dominant, there are three conditions or properties, first one is…

Q: What are L and D (the diagonal pivot matrix) for this matrix A? What is U in A = LU and what is the…

A: In the given question, the matrix A is given as: A=248039007D=diagA=200030007

Q: Find an LU factorization of the matrix A. 3 -1 3) A- - 18 1 0][ 3 1 A) A= B) A = 10 3 -1 0-3 -6 1 0…

A:

Q: Find all a and B >0 so that the matrix B = 23 6 2 is diagonally dominant;

A: A square matrix is diagonally dominant if   for .

Q: (3 (4") *) If A is 3 x 3 matrix with det (A) = 3, find det %3D

A:

Q: 4. (a) Show that the following matrix is diagonalizable. (b) Find a matrix P that diagonalizes A.…

A: Given:

Q: [5 Let B =E dl: Is the matrix B orthogonally diagonalizable? If yes, find a diagonal matrix 2 0…

A:

Q: C be the matrix defined as a₁ an C = a-1 9₂ az az a a₂ a, a az a4 1 A an an-l an-2 a₁

A:

Q: 4. (a) Show that the following matrix is diagonalizable. (b) Find a matrix P that diagonalizes A.…

A: A matrix is said to be diagonalizable if the algebraic multiplicity of the eigen value is same as…

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