Construct the matrix with rank one that has Av = 12u for v = ½(1, 1, 1, 1) and u= ½(2, 2, 1). Its only singular value is a1 = __ .

Q: a Verify that det EA = (det E)(det A), where E is the elementary matrix shown and A =

A: E=1k01  A=abcd

Q: Consider the 6 × 8 matrix 3 0 0 0 0 1 2 1 0 0 0 0 1 0 0 -3 4 -7 -9 A = 0 0 0 0 0 0 0 0 0 1 8 1 and…

A: The main objective is to answer the sub parts by using given matrix which is in reduced row echelon…

Q: Find the characteristic equation of the matrix by inspection. 4 2] -6 0 0 6 0 0 5] 4 -9 LO

A:

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: Find a condition on a and b, such that the symmetric matrix A %3D has only ositive eigenvalues

A: In the given question we have to find the condition on a and b, such that the symmetric matrix has…

Q: Find an LUfactorization of the given matrix.

A: To Determine: find an LU factorization of the given matrix  Given: we have a matrix12-3-1…

Q: Let A be a matrix with singular values {1, 2, 3,..., 2022}. Find the singular values of the matrix…

A: Given,     A = [ 1, 2, 3, 4, . . . . . . , 2022]

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: find the eiganvabes and normalised eisenvektörs for each of the Following matrices i) 2. --4 -3 -4 3…

A:

Q: Compute the rank and nullity of the given matrices over the indicated Zp

A:

Q: The multiplicative identity matrix of order 3 is I3 =_______.

A: Let the Identity matrix be…

Q: Suppose that an nxn matrix A has a QR-decomposition where

A:

Q: 4. Find the standard matrix for T where Ta2) =(2x,+x -2,).

A:

Q: VýB × VA

A:

Q: [1 2 2 3 1 0 1 1 4 4

A: Given matrix is  123101144find LU factorization of a given matrix

Q: 5. Find a dlagonalizes the fouowing natrlx A, and determine the diagonal matrix D = p'AP matrix p…

A:

Q: Find the change of basis matrix from B2 to B1. -4 B1 = , B2 B2 = 2

A: The change of basis matrix C from B2 to B1( or from the basis B2 to the basis B1 ): β1=-142,231  and…

Q: Let A be a 3x3 diagonalizable matrix with eigenvalues: 1, = 0 with corresponding eigenvector v, ,d2=…

A: Given that A be a 3×3 diagonalizable matrix with eigenvalues λ1=0 with corresponding eigenvectors…

Q: What is 'a', if B as shown below is a singular matrix?

A: A singular matrix is a matrix whose determinant is zero.

Q: Find the characteristic equation for the matrix 2 (13). and use it to compute M-¹. M

A:

Q: (2) Let A = UDV" be a SVD of a square matrix A. What is the sum of squares of the singular values,…

A: We find the sum of squares of the singular values in terms of A.

Q: Consider A = 21 2 1 3 -1 -3 4 Convert A to an upper triangular matrix U by using Gaussian…

A:

Q: Enter a 3 x 3 symmetric matrix A that has entries au = 5, az2 = 4, a33 = 0, a12 = 2, a3ı = 1, and…

A:

Q: Find the canonical form B and an invertible matrix P such that P−1AP = B.

A: In this question. we find the invertible matrix P and B such that P-1AP=B

Q: Let A be a 7 × 5 matrix of rank 4. Let P and Q be theprojection matrices that project vectors in R7…

A:

Q: Let A be an n x n matrix that is similar to an upper triangular matrix, and that has the distinct…

A:

Q: Prove det(A) = det(A'), for an upper triangular matrix A.

A:

Q: Suppose A is a matrix with eigenvalues A1 = 1, A, = 2, A3 = -3, with corresponding eigenvectors v1…

A: Given: A is a matrix with eigenvalues λ1=1, λ2=2, λ3=-3 with corresponding eigenvectors v1=001,…

Q: Find value(s) of ß for which the matrix A is singular. —3 - в |-2 B 1 1

A: Given:         A=β-3-β-2β1β10    A matrix is singular if and only if the determinant of a matrix is…

Q: For the matrix A, find (if possible) a nonsingular matrix P such that P-AP is diagonal. (If not…

A:

Q: 18. Let A be a 3 x 5 matrix with 2 pivots. What is the dimension of Nul(A)?

A:

Q: Suppose A +A+I-0 where A is a square matrix then A= A -A-I -2A A-I CS Scanned with CamScanner

A: Now we will find A-1 . Where I is identity matrix.

Q: In all parts, suppose that A is a matrix of size 11 x 8 (i) Assuming that rank(Atr) = 3, determine…

A: It is given that

Q: 2. Let the rref of a matrix A be, 0 2 0 -2 0 1 -5 0 -3 0 0 0 1 6 Determine A if the first, second…

A:

Q: Consider the matrix -1 3 containing the eigienvectors for the coefficient matrix 0.978 -0.006 0.004…

A:

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

A: Given:

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: Let A be a 3 × 3 matrix whose first row entries are a11 = 1, a12 = 2, and a13 = 3. Suppose 1 1 0 3 2…

A:

Q: Let A be a nilpotent matrix of order n then A*n = 0 ) nxA = 0 A =nx1, l is Identity matrix

A: A be a nilpotent matrix of order n

Q: O Find the transforma tion matrix that wotates the axis X of a rec tangu lar coor dinale system 60…

A:

Q: 2. Choose the rank of the matrix AT

A:

Q: Find the coordinate matrix of x relative to the orthonormal basis B in R". {(금, 승 이) (-승름이 (0,0, 1}…

A:

Q: Determine LU decomposition and Cholesky LLT factorization of the matrix -1 A = -1 -1 -1 2 where E is…

A:

Q: Find a matrix P that orthogonally diagonalizes A, and determine P-'AP. A = 1 4 P = P = 2 V3 V3 2 P =…

A: First we need to find eigen values:

Q: Find the singular values of the given matrix.

A: Consider the given matrix, A=2102

Q: Let A be the 2 x 2 matrix with elements a,, a12 = a21 = + 1 and a,, = - 1. Then the %3D eigenvalues…

A: Introduction :Given , a matrix A with elements and we have asked for the eigen values of matrix A19

Q: If A is a 3 x 3 matrix with Eigen values, x, y, z then the Eigen values of A are 1 1 1 (a) y.z (b)…

A: Please see the explanation below

Q: If A is an n X n matrix with linearly independent columns, then R" has a basis of linearly…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: - L

A: Given that A=42-12 Take  A-λI=04-λ2-12-λ=0(4-λ)(2-λ)+2=08-6λ+λ2+2=0λ2-6λ+10=0λ=6±36-402λ=6±2i2λ=3±i

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.