Verify that the following matrix is an Orthogonal Matrix: cosø sinø sin Osinø cos0 -sin@cosø -cos O sinø sin 0 cosocosø

Q: Let a Consicler the matrix 121 4) S23. A=/S. 87.3 Find Miz, Ci2 and M2z Czt

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Q: Determine whether the following matrix is orthogonal or not: cosa sina A = sinßsina cosß -sinßcosa…

A: To determine if a matrix is orthogonal or not, multiply the matrix by its transpose. If the…

Q: a) For invertible matrices A, BER"Xn, show that ((AB)")- = (A-)"(B)".

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Q: Let A and B be 2x2 matrices such that B is invertible If detA)2 and det)-, then detA'e) Select one:…

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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: The matrix of cofactors of A is precisely [adj(A)]' O True O False

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Q: Verify that the following matrix is an Orthogonal Matrix: cosø sinø sin O sinø cos0 -sin@cosø…

A: To verify: The matrix is orthogonal Matrix. Given: The matrix is cos ϕ0sin ϕsin θ·sin ϕcos θ-sin…

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…

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Q: Consider the given matrix. Determine det(A) and the inverse matrix of A.

A: Here we have to find the determinant and inverse of a matrix.

Q: let Amxn matrix , c scalar If cA=0, then Select one: a. c=0 and A=0 b. c=0 or A=0 C. C0 or A=0

A: WE have to check the meaning of cA=0.

Q: Find the coordinate matrix of x in Rn relative to the basis B′.B′ = {(4, 0), (0, 3)}, x = (12, 6)

A: Given B′ = {(4, 0), (0, 3)}, x = (12, 6) Let the coordinate matrix of x in Rn relative to the basis…

Q: Let A be an n × n matrix and let Q and V be n × northogonal matrices. Show that ||QA ||2 = ||A ||2

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Q: Verify AB = BA for the matrices below. – sin a cos B - sin sin B CO A | A = and B sin a CO A Cos 3

A: Please see the answer below.

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

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Q: Express the following matrix as a product of several elemen- tary matrices. 1 3 E 2 3 ||

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Q: Suppose A is a matrix such that A² + A = I, I is the identity matrix. Show that a) A must be square.…

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Q: det(cA) = c det(A) Insert a number to sho

A: Given that  A is an n×n matrix and c is a scalar. Check whether detcA=cdetA is true or false.

Q: Find the Jacobi matrix for the following function. 5x + 6у f(x, y) = 5x - 4y? Jacobi matrix, (Df)(x,…

A: Given : f1(x, y) = 5x+6y f2(x, y) = 5x²-4y² To find : Determinant of jacobian matrix

Q: Let A and B be square matrices of order n. Suppose B7 = b has no solution for some 6ER". Prove that…

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Q: for any conformable matrices A, B, and C, the equation (ABC) = C'B' A' holds. 4. Given the following…

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Q: Let A be an nxn matrix, then for any n EZ*, det( A")= (det A)" . Select one: True False

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Q: Let A be an nxn matrix. If A-= det A adj A is computed, what should AA be equal to in order to…

A: Using the given matrix equation we need to find the value of AA-1 .

Q: Г1 3 2 5 1 [3 4 2

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Q: I find the cooridinate matrix for A realtive to S=SA, Ag „Az, Au? where A= [2 0 and 1 1 00

A: The coordinates matrix for A is [a b c d]=aA1+bA2+cA3+dA4=A .see 2nd step.

Q: Compute det(Ei) if Ei is an elementary matrix of type i.

A: Elementary matrix is the type of matrix which is formed by changing one row of the identity matrix.

Q: Verify by finding the matrix of S 0 T (a) by direct substitution and (b) by matrix multiplication of…

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Q: Assuming that all matrices aren xnand invertible, solve for D. BCA DCB'A = BC?.

A: Properties of invertible matrix:  If a matrix A is invertible and then there must exist a matrix…

Q: If UT = U-1, then matrix U is an orthogonal matrix. %3D O True O False

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Q: Consider the following matrix: A-() 1. Determine whether A is diagonalizable over C. If so,…

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

Q: 2) Let B and C be bases for R2. If B = {(-1, –1). (2. – 1)} and the change-of-basis matrix from B to…

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Q: Let A be the 2 x 3 matrix with entries aij = (i – 1)(j+ 1). Which of the following is the matrix A?

A: A be a 2×3 matrix. This means A2×3 . entries of matrix A are ai,j=(i-1)(j+1)

Q: Find the cofactor matrix of the following matrix 1 0 1 A = 4 -2 5 1

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Q: Let ß = {b1, b2} and C = {c1, c2} be bases for R?. Find the change-of-coordinates matrix from ß to C…

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Q: Let B = and B' = Find the change of base matrix from B' to B and from B to B'

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Q: ue? 0 0.

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Q: Determine whether the matrix A = -1 is diagonalizable. If it is diagonalizable, then find the…

A: The given matrix is  A=010-100002 Finding the eigen values of the given matrix…

Q: Let B and C be bases for R?. If B = {(-1,–1), (3, 4)} and the change-of-basis matrix from B to C is…

A: We are given B = { (-1, -1), (3, 4)} basis of R2 and a matrix PB→C =1-1-12 We need to find the basis…

Q: If G = | is alx1 matrix, and A is a 1xn matrix, is it true that XA = GA for %3D any number A. Is it…

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Q: 4. Let Q E Rxn be an orthogonal matrix. Show that ||Qx||2= ||||2 for %3D any x E R".

A: Given that  Q∈ℝn×n be an orthogonal matrix.

Q: Q3, Write any matrices A and B of order 3 x 3 and verify the results Let A and B be n x n matrices,…

A: Write any matrices 'A' and 'B' of order 13×3 A=110012003    B=013100100 To verify 1)…

Q: Consider the matrix B given by 0 0 0 B = 1 0 0 0 1 0 Show that B3 = 0. Also, compute for the product…

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Q: Use the matrix capabilities of a graphing utility to find the inverse of the matrix (if it exists).…

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Q: Let A, Band C be square matrices Such that AB = AC, If A#0,then B-C. 1s this True or false? Explain…

A: Let A, B, and C be square matrices such that AB=AC. If A≠0 , then B=C. Determine true or false.

Q: Let A be nxn orthogonal matrix and v E R". Then ||Av||? = || ||?. %3D Select one: True O False

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Q: Assume that T and S are matrix of the same size. Prove or Disprove that (T + S) 2 is a symmetric,…

A: Given   T  and   S are matrix of same size. We have to prove if  T+S is symmetric, skew - symmetric…

Q: Let U be a square matrix such that U'U=I. Show that det U = +1. Assume that U'U=1, Since the desired…

A: Given; UTU=1 The objective is to shown that det U=

Q: Let B and C be bases for R. If B = {(-1, -1), (3, 4)} and the change-of-basis matrix from B to C is…

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Q: Let A be a 6 x 5 matrix. What must a and b be in order to define T : Rª → R* by T(x) = Ax? II

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Q: Complete the matrix A so that it is Hermitian. 6 – 3i 1 A = -4 1 2 2 =

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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.