a11 a12 a13 such that a23 Let Z be the set of 2 x 3 matrices a21 a22 a11 + a12 + a13 + a21 + a22 + a23 = 0. %3D a12 a13 Let R be the set of 2 x 3 matrices such that a21 a22 a23 a11 + a12 + a13 = a21 + a22 + a23 = 0. a12 a13 Let C be the set of 2 x 3 matrices such that a21 a22 a23 a11 + a21 = a12 + a22 = a13 + a23 = 0. Find bases for Z, R,C, R+ C, and RnC and determine their dimensions..

Q: Express as a single matrix.

A: The matrix we have is  2014-2302-3451

Q: Express the quadratic form (c₁r1 + c₂2+...+Cnn)² in the matrix notation TA, where A is symmetric.

A:

Q: Show that A and B are not similar matrices

A: Given matrix is The characteristic polynomial of matrix A is

Q: Multiply the given Matrices

A:

Q: Let A and B be two square matrices of the same size. Prove that det(AB) = det(BA).

A: Using Determinant and elementary row operations,

Q: Construct six linearly independent 3 by 3 echelon matrices U1, ... , U6.

A: To Find : Construct six linearly independent 3×3  echelon matrices.

Q: Determine whether or not the matrices [5 -3 [5 -1 2 -1 and |4 1 -2 are similar. 3 |2 -1 2 Choose

A:

Q: b) The following proposed proof contains two mistakes. Explain the mistakes. Result Let A and B be…

A:

Q: Diagonalize the following matrix: 1 7 - 1 13 5 -5 -7 - 1 7 not diagonalizable 6 0 0 -9 0 0 - 12 90 0…

A:

Q: Let A, B, and C are 3 x 3 matrices and det(A) = -2, det(B) = -6, det(C) = 1. Evaluate the following…

A:

Q: Let 2 -1 | -1 2 -1 -1 -1 -1 -1 –1 -1 2 -1 2 be the Eç Cartan matrix corresponding to the simple…

A:

Q: Let X be a 3 x 4 matrix, let Y be a 4 x 4 matrix and let Z be a 4 x 3 matrix. Select all of the…

A:

Q: Find the following matrix product. Be careful to distinguish 2 x 2 matrices in the answers from 2 x…

A:

Q: -3 (49) (3) (-3) 4 120 1030 0205 245 0 5 6 3040 0 50 6

A:

Q: Find ∣A−1∣ for the matrix

A:

Q: Let A.3 be 5x5 matrices such that det (A) = 7 and det(A)=-3. Find the following (1) det(2(A^B)')…

A: if A is an n×n matrix and det(A)=a thendet(kA)=kn×adet(A-1)=1adet(AT)=adet(adj A)=an-1

Q: Find all matrices A = (a,b;c,d) that satisfy A(1,1;1,1) = (1,1;1,1)A

A:

Q: Find all matrices B that commute with 1 + i (¹+1) :). 0 A = That is, for which AB = BA.

A: Let B=abcd be the matrix such tghat AB=BA

Q: Express as a single matrix.

A: Here we need to express the product of matrices 2-1030-22-13030142as a single matrix.

Q: 1 0 2 -2 3 1 3X +|2 1 3 -1 -2 0 4 -1 5 1 5 II

A: The given equation is,

Q: ebra to show that for n x n matrices A,B,C and n x 1 vector rtible and ABC then the matrix equation…

A:

Q: Find A-E and the elements from the matrices

A:

Q: In the inner product space of 2-square matrices, with the inner product <uv2 trlu the two matrices…

A:

Q: Let A and B be square matrices of order 3 such that |A-| = x + 7 with x + -7 and |A * A" | = . What…

A: A and B are square matrices. Therefore, det(AB)=det(A).det(B) det(A)=det((A)T) We will use these…

Q: nts) Check the definiteness of the following matrices A and B; -1 1 1] A = |1 5 L3 0 5 0 B = 3 -1 2…

A:

Q: 4 = = - (13 + 2) 0 3 13 -13 13 + 2 0 9. 1 B = 1 13 +3 4 -(13+ 4) [13 13+1 1 0 Calculate the…

A: Matrix multiplication is defined as row by column multiplication where the elements of the ith row…

Q: 0 A2 0 and P = [v1, v2, V3] and show that 0 0\3 Construct the 3 x 3 matrices D AP = PD.

A:

Q: write the given permutation matrix as a product of elementary (row interchange) matrices

A: We have the given matrix We need to write A as a product of elementary matrices.

Q: N.N て1 て てー -3 こ 1. そー ) Find oenk of the matrix p

A: See the attachment

Q: ow that (ABC) = CTBTAT by using the fol

A:

Q: 7/13 los (e) 2

A:

Q: The following Matrix represents the supercoach points scored per round of three AFL players from…

A: The matrix is obtained from the table by arranging the values in the rows and columns. The new…

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.