(1) For the matrix A below, find 2 x 2 matrices P, B such that P-1 AP (canonical) form. B and B is in Jordan normal -4 4 (0) A =

Q: (b) Find the characteristic equation of the matrix P defined by [2 1 1] P = 1 2 1 li 1 2] Further…

A: The given matrix is P=211121112 the characteristic equation is given by P-λI=02-λ1112-λ1112-λ=0…

Q: 3. Given a vector x = (0 4 a), where a is the last digit of your Roll number. Find a Householder…

A: Given that x=0 4 7T. The Holder matrix is given by Hx=I-2xTxxxT Hence the Holder matrix is…

Q: S = Consider the matrix -1 1 1 1 0 [33 3 Find an orthogonal S such that S-¹ AS = D, a diagonal…

A: Given A=0330 and S-1AS=D, a diagoanl matrix

Q: A Hessenberg matrix H, is n X n matrix that has 2 on the main diaonal, 1 everywhere below the main…

A:

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: For A a square matrix such that ATA = I show that det A = ±1.   If A is square and A5 = 0 show…

A: Given, ATA=IdetATA=detIdetATdetA=1  Since, detI=1detA·detA=1    Since, detAT=AdetA2=1detA=±1 This…

Q: Find a 3 x 3 matrix A such that Ax = 9x for all x in R3. A II

A:

Q: 4. Find a real-valued fundamental matrix for y' = Ay where [2 1 0 0 2 0 |0 1 A =

A: Given: A=210020012

Q: The mist Consider ann x m matrix A. Find dim(im(A)) + dim(ker(A")), in terms of m and n.

A: Please check step 2 for the solution.!

Q: For the matix A given below, calculate (A-I)T (where I is the 3 x 3 identity matrix). A = 2 -1 0 5…

A:

Q: Let A be an n × n matrix. Is it possible for A2+I = O in the case where n is odd? Answer the same…

A:

Q: SP6 Find the condition number of the matrix from SP3 using the 1- norm. SP3 Given the matrix a -1 2…

A: Solution:

Q: Given the matrix 1 1 1 2 -1 0 0 0 3 1 1 4 A = Consider transforming A into an upper triangular…

A:

Q: Compute the product M (0)0 (7) as a 2 x 2 matrix. What kind of isometry is this product?

A:

Q: 5. Give 2 x 2 matrices A so that for any x e R² we have, respectively, (f) Axis the vector obtained…

A:

Q: (2) Consider the matrix -[: ] A = Find the unique x, y E R, such that A? = xA – yI (where I…

A:

Q: A Hessenberg matrix Hn is n x n matrix that has 2 on the main diaonal, 1 everywhere below the main…

A:

Q: [2ß ß Find all the values of the parameter ß for which the matrix is 3 5B] Consider invertible.

A: The matrix is given as , A=2ββ35β find all values of β for which the matrix is invertible.

Q: 8. For the column matrix v=(v₁) we have explain then: (VA); =Vkaki

A:

Q: A Hessenberg matrix H, is n x n matrix that has 2 on the main diaonal, 1 everywhere below the main…

A: As per the instruction, we will be answering only the first one. For (a), det(H2)=det2112…

Q: 1- nullspace af now equivalent to the for the 1 1- 2. C. that puy -2 B. assume matrix pand Let A

A:

Q: [3 Compute the mnatrix exponential et for the diagonal matrix A = %3D

A: We have to find the exponential matrix of given diagonal matrix

Q: nofthe following is a product of elementary matrices for the matrx 1 0 4. 11 T-1-1 01 0 1 -2 1. 1 4…

A: We have to choose the correct answer from the given option according to the given condition

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

A:

Q: Find a matrix P such that P- 0 3 1 0 O A 1 P = OB. %3D 1 1 1 P = 0 1 OC. ODP= 1 0 -1 0 1 1 P %3D

A:

Q: The 2 dimensional, first-order, linear-homogeneous and autonomous equa- tions, a11+a12y] a21+ a22y…

A:

Q: Let A be n X n matrix that has zeros on the main diagonal and ones everywhere else. Example of a 4 x…

A: Introduction: The inverse of a matrix is another matrix that yields the increasing identity once…

Q: A real square matrix Q is called orthogonal if QTQ = I. Prove det(Q) = ±1. Give an example of such a…

A: Solution

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: 2. Find a real 2 × 2 matrix A (other than A =I) such that Aº = I . %3D

A:

Q: Q3. In the triangular decomposition of a symmetric nxn matrix (in the form of LL"), the number of…

A:

Q: Let A be n x n matrix that has zeros on the main diagonal and ones everywhere els a 4 x 4 matrix of…

A: Inverse matrix:  The inverse of a matrix is another matrix that yields the multiplicative identity…

Q: 1.0 T(A) = 2AX - 2XA, where X is a fixednxn matrix %3D n,n mation ansformation

A:

Q: [1 1 1 x is invertible. %3D Determine the values of x so that the matrix A

A: To determine the value of x so that the matrix A=11x1xxxxx is invertible. Solution: A matrix is…

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: 0. LetA 8 l show that there are no 2 x 2 matrix B such that %3D B2 = A. %3D

A:

Q: Assume A and B are two m × n matrices with the same reduced echelon form. Show that there exists an…

A: Given A and B are two m×n matrices with the same reduced echelon form. We have to show that there…

Q: Let x and y be square matrices of order n a. Show that if x and y are skew symmetric, then x + y is…

A:

Q: A Hessenberg matrix H, is n x n matrix that has 2 on the main diaonal, 1 everywhere below the main…

A:

Q: - Let A be the n x n matrix with all I's on the diagonal and all 0's above and below the diagonal.…

A:

Q: Q 2 For each matrix 1 0 0 C = 2 2 0 0 1 0 31 1+i A = B = 0 2 2 1-i 2 002 Discuss whether the given…

A: as per our guidelines we are supposed to answer only 3 subparts if there are multiple subparts are…

Q: For the matrix A , there is an invertible matrix P such that P^(−1)*AP = D, where D is a diagonal…

A: Given matrix is A=−505−744−111, P=36113113111 and P−1=−170−202−2835−7730−355. We have to compute…

Q: For purposes of this exercise, let us define an "X-matrix" to be a square matrix with an odd number…

A: Given that: X=101010101

Q: ind LU and LDU factorization of the following tridiagonal matrix. A=[1 1 0; 1 2 1; 0 1

A: Given matrix is  A = 110 121 012 To find the LU and LDU factorization of the given matrix.

Q: Prove: NS(A) = NS(ATA) for any matrix A. You have actually done this already in the homework, but…

A:

Q: 1. Let Y = [Y1 Y2]T and X = [X1 X2]T be two random vectors such that Y = AX, where A is a 2 × 2…

A: Let A=a11a12a21a22, it is given that Y=Y1  Y2T=Y1Y2 and X=X1X2T=X1X2 so it follows:…

Q: A Is an ortn A has orthonormal columns A has orthonormal rows A is square matrix iv. i. ii. iii. A…

A: If A is an orthogonal matrix then which of the following is true. 1. A has orthogonal columns 2.A…

Q: Which of the following is true or false? a)An orthogonal and symmetric matrix Q satisfies Q2=I…

A: a Since Qis orthogonal matrix. ⇒QTQ=I ...i and Q is symmetric ⇒QT=Q ...ii Now, substitute the value…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.