Let A, B, C be (3 x 3) matrices, such that det(A) = 2, det(B) = 7, det(C) = 1. What is the value of det(3ATB-A-C) ?

Q: Due to what property, applied to the matrices below, do we know that A + (−A) = O?

A: A+-A=O

Q: Find an SVD of the matrix. -6 5 A = 0 6

A: We have to general eigenvalue and eigenvectors to find Singular Value Decomposition of matrix A We…

Q: Let A, B, C be n x n matrices. Verify that (a) A is similar to A. (b) If A is similar to B and B is…

A: Given A, B, C be n × n matrices

Q: Find an LU factorization of the matrix A (with Lunit lower triangular). 4 -8 8 -4 A = 8 - 14 11 -5…

A:

Q: Let A be an nxn matrix and B= A+ I, where / is the identity matrix, then it is possible for A and B…

A:

Q: Find the LU factorization of the matrix A, where 3 -5 2 3 2 -2 A = -1 -6 1 -1 -4 1 2 1 2.

A: We know that A = L U where L is the lower triangular matrix and U is the upper triangular matrix.

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: find an LU factorization of the given matrix.

A:

Q: Find a sequence of elementary matrices whose product is the given nonsingular matrix.

A:

Q: If A and B are invertible 5x5 matrices, then A+B is also invertible. True False

A:

Q: (4) For the zero-one matrices A = and B = calculate %3D 0 0 1 1 (а) АЛВ (Ъ) АоВ (с) ВОВ

A: 4) Note:  AΛB = [aijΛbij] =[aijbij] , known as meet of A and B, only possible if matrix have same…

Q: Due to what property, applied to the matrices below, do we know that A + B = B + A?

A: Due to Commutative Property Of Addition of matrices, we can say that: A+B=B+A. Where, A,B,C are…

Q: Find a 2 x 2 orthogonal matrix P whose first row is a multiple of (a) (3,–4), (b) (1,2).

A: Result: Rows (columns) of an orthogonal matrix are an orthonormal basis. Hence, each row (column)…

Q: Find the inverse of the matrix using Gauss Jordan method?

A:

Q: What is the name of the matrix, Sij?

A: Sij is called as similarity matrix.

Q: Given a 2 by 2 matrix, how do i show that it is a linear combination of unitary matrices

A: See the attachment

Q: Show that AB and BA are not equal for the matrices

A: Given: The matrices are given as, Finding the value of AB by using matrix multiplication,

Q: Write down the necessary conditions for the matrix B2*2 (2 ∗ 2 matrix) to have an inverse matrix.

A: Necessary conditions for a 2*2 matrix to have an inverse matrix.

Q: Let A, B, and C be three nonzero n × n matrices such that AC = BC. Does it follow that A = B? If so,…

A:

Q: What does it mean to say that A is a matrix with dimension m x n?

A: Our Aim is to tell that what is meant by a matrix A which is havingdimension m×n.

Q: When the inverse of a matrix is multiplied by the original matrix, it produces the: A. matrix of…

A:

Q: If A=XDX−1 where  X is a diagonalizing matrix of A, then 7X is also a diagonalizing matrix of A.…

A: Given: Where, X is a diagonal matrix of A, then 7X is also diagonalizing matrix of A. To determine:…

Q: Find a matrix B in reduced row echelon form that is rowequivalent to A, using elementary matrices.

A: Given- 2-40013006 To find- Find a matrix B in reduced row echelon form that is row equivalent to A,…

Q: Let A be an n xn matrix and B= A+ I, where I is the identity matrix, then it is possible for A and B…

A:

Q: Find an LU factorization of the matrix A (with L unit lower triangular). 4 - 4 2 - 8 2 - 1 A = 10 8…

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: Given two matrices A and B, how can you determine the order of AB, assuming that the product is…

A: Let order of A is mxnAnd let order of B is nxp (because product of AB is defined)

Q: 3. Is the trace of the product of two square matrices equal to the product of these two matrices'…

A:

Q: Give an example of a 3 x 3 upper triangular matrix A that is not diagonal. A =

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: Given two nxn matrices A and B, what are the criteria for the matrices to be inverses?

A: Given the matrices A and B of order nxn.

Q: If A is a nonsingular matrix whose inverse is 4 find A.

A: Given  The  A  is a nonsingular matrix  whose inverse is 2141.

Q: Compute the product AB by the definition of the product of matrices, where Ab, and Ab, are computed…

A: We will use the product method of matrix to find solution to the problem .

Q: Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, [1 3 -2]…

A: A=13-223001-1

Q: Let A and B be matrices with size 3 x 3. If only one of these matrices are diagonalizable and if…

A: Given, A and B be matrices with size 3×3det(A-λI3)=(λ-2)(λ2-9)det(B-λI3)=(λ-3)2(λ+2)(a) Eigenvalues…

Q: Formulate the method for adding partitioned matrices, and verify your method by partitioning the…

A:

Q: What is the linear combination of the matrices аnd

A: The explanation are as follows

Q: Let A, B, C be n x n matrices. Show that if A is similar to B and B is similar to C, then A is…

A:

Q: Find the inverse of the matrix and verify that A-!A = AA1- 1. 4--10 A 3D 2. 8. A-1 Show My Work…

A:

Q: Find an LU factorization for the matrix: 1 2 1 2 1 2 -2 0 1

A:

Q: Find two 2 × 2 matrices such that ∣A∣ + ∣B∣ = ∣A + B∣.

A:

Q: Compute the product AB by the definition of the product of matrices, where Ab, and Ab, are computed…

A: We have to find the product of the given matrices  [ A ]3×2 and [ B ]2×2  with b1 and b2 be the…

Q: Find the LU factorization of the matrix A, where 3 -5 2 -2 A = -1 -6 1 -4 1 2 1 2. 2.

A: Given matrix is A=−23−5232−22−1−61−1−4121. We have to find the LU-factorization of the matrix A. By…

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: Find the nullspace of the matrix given as; A=[1 -2 1; 2 -3 5; 1 0 7]

A:

Q: If A and B are invertible 2 × 2 matrices with nonnegative entries, then A + B must also be…

A: Let's take one counter example of the given conditions. That is A and B are invertible 2*2 matrices…

Q: Suppose A, B, and C are three non-zero square matrices such that AC = BC. Is it true that A = B? If…

A: Not true

Q: If A, B are two n x n orthogonal matrices, then AB is also an orthogonal matrix. True False

A: Give:  If A , B are two n×n orthogonal matrices. To check: product of matrices A and B are…

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.