The trace of a square matrix A, denoted by tr(A), is defined as the sum of the main diagonal e of A. If X and Y are n-by-n matrices, which of the following is a true statement? (b) If tr(X) = 0, then X = On- (d) tr(XY) = tr(YX). (a) tr(X²) = [tr(X)]². (c) tr(XY) = tr(X)tr(Y).

Q: Let A be a 5 x 5 matrix with det(A) = -10. 1. If the matrix B is obtained from A by adding 4 times…

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Q: c1x1(a) + c2x2(a)+ . . . +cnxn(a) = x(a). Let X (t) be the n x n matrix with column vectors x1, x2,…

A: Given : Xt be any  matrix of n×n           : c be column with component c1 ,c2 , . . .  . . .  ,cn…

Q: 3. (a) Solve the matrix equation for X: -1 0 1 1 2 1 1 -3 1 -1 3 1 -1

A: If Ais a m×n matrix and B is a n×p, then AB is m×p Hence here X is 2×3 Let X = abcdef Thus…

Q: If (X– A)(B – C) = D where all matrices involved are invertible square matrices, then: (A) X = + A В…

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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: Let A, B be  matrices of the same order. Then det(A+B)=det(A) + det(B).  True or false

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Q: 3) Consider the following matrix: A= 220 001 0 10 - 1 1 (i) Compute A™ ¹. (ii) Write A as a product…

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Q: Let A = 1 (a) BA = (b) AB = 0 0 2 Find each matrix below. If a matrix is not defined, click on…

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Q: Some of the entries of the 3 x 3 matrix A are known as A -1 1 If det (A) = -–6 and A-1 find x.

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Q: Let A and B be 3 × 3 matrices such that det (B) = -2 and 27 = det (-3AB A" B ²). 2 Find det(A).…

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Q: Find the inverse of the given matrix using Adjoint Matrix: 1 -1 0 0 -1 2 -1 0 0 -1 2 -1 0 0 -1 2

A: We know A-λI = 0 A-λI =    1-1   0   0-1   2-1   0  0-1   2-1  0  0-1   2-λ1000010000100001 = 0

Q: Suppose that B is a square matrix with det(B) = -2. Find each of the following. (a) det(B6) = (b)…

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Q: 3. Let A, B € Mnxn (F) be n x n matrices. (a) Prove that tr(A + B) = tr(A) + tr(B). (b) Prove that…

A: Trace of matrices is sum of its  diagonal entries

Q: A=(41] [4] ( )= (-1) [₂] + (3) [₂] 2

A: Matrix multiplication is possible if we have two matrices A and B such that, order of A =m×n;order…

Q: (18) Does a 2 × 2 diagonal matrix commute with every other 2 × 2 matrix?

A: We have to check

Q: [123] Find the inverse of matrix A using the equation A² - 5A - 21 = 0 where A = 12

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Q: adioint of the matrix.

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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: Consider the following function; Q(x1, x2, X3) = 2x? + 3x? – xž + 5x1x3 + x2x3 Find the matrix A…

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Q: ind the 3x3 matrix that is equivalent in it's action to each of the

A: Given: To find 3×3 matrix that  equivalent to the symmetry operators are, a  S^2zb  C^2z

Q: Solve the matrix equation Ax = 0, where

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Q: (4) Let A be a 3x3 matrix. If |4|= 2 , then |3.4|=,

A: Given that A be a 3*3 matrix and |A|=2. To find the value of |3A|

Q: If A = B x C, find the matrix A. B [ 1 -3 -2 201 C ·[ 2 -2 3 1 -1 0

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Q: Provide the symmetric matrix that generates the following quadratic form Q(x): x+2x+3x3 + x₁x2 - 2X1…

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Q: C is the curve y = e® from (2, e²) to (0,1) and F = (x², -y), compute ſ, F-dr.

A: Given that, C is the curve y=ex from 2,e2 to 0,1 and F=x2,-y Then, F=x2,-y=x2,-ex So, F→=x2i^-exj^

Q: (d) Express 2 as a linear combination of Y1 (e) Express 2 as a linear combination of L93 (HB)). (0)…

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Q: -1 Suppose A, B, C, X are invertible n x n matrices. Solve the matrix equation C(B1X) = (B-²C-1) B²…

A: If A and B are nxn invertiable matrices then(AB)-1=B-1A-1

Q: 3 If A= 2x+ x- is a symmetric matrix, then x ? 3 x+2 (A) 4 (B) 3 (C) -4 (D) -3 O A

A: we have given A is a symmetric matrix.  We have to find the value of x