Question 2. Let P be an orthogonal matrix. (a) Prove that det P = 1 or det P = -1. (b) If det P = -1, show that I+P has no inverse. Hint. Show that P"(I +P) = (I + P)'.

Q: 3| |1 Let A 3 1 4 3 1 3 41 1) Verify that: AadjA = det(A) I (Where I is the identity matrix) 2) Find…

A: given matrix isA=1331431341) to verifyA.adj(A)=det(A).I2) to find A-1

Q: l8h Will save this response Question 7 Let A be a nonsingular matrix. If det(A) =3, then det(A1) =…

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Q: Question 2 a) Find the upper triangular matrix that satisfies |1 30 A' b) Let and 6 = 1 q 0 1 a =| P…

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Q: (1). Find an elementary matrix E so that B = EA where %3D [1 0 B= |0 1 -5 16] 7 A=0 1 L-2 0 2 -5

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Q: Question 2 For what value(s) of k is the matrix not invertible? Blank 1 Blank 1 Add your answer kk 0…

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Q: -5 -1 5 Let A = -6 -8 be the matrix of T:P, - P, with respect to the basis B = {v,, v2, V3}, where…

A: We can use the definition of matrix representation of linear transformation

Q: Question 5. Find all values of a e C such that 1 0 1 A(x) : 0 1 0 0 1 is a positive definite matrix.…

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Q: 1. Gegeben sei die Matrix A = 0 1 (a) Ermitteln Sie A?. n (b) Zeigen Sie mit vollständiger…

A: we have to show that the following

Q: Question 9 101 v-1 s an elgenvector of the matrix A- 0 11 correspondng to the elgenvalue A- 110

A: The solution is given as

Q: 0. -1 Compute the inverse of the matrix A = -1 -3 -4 Type DNE if A is 1 1 1 not invertible.

A: We have given  matrix  A=0-1-1-1-3-4111 Then, A=0-3+4+1-1+4-1-1+3   expand along R1=3-2=1…

Q: Question 2 Which of the following is NOT equivalent to the statement "The n xn matrix A is…

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Q: Question 7 Let A be a square matrix. ( a) If A' = 0, show that I-A is invertible. (b) Suppose…

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Q: 1 0 1 to diagonal | Find a matrix P which transform the matrix A= 1 2 2 form. Hence A. 3. 2.

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Q: 5. Let A- (, ) -(). 1 and a = Consider the matrix equation Ag = ke where k E R. Then the scalar k…

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Q: If p(t) = co + Ct + c2t +...+ Cnt", then define p(A) to be the matrix formed by replacing each power…

A:

Q: snip

A: Given matrices are 110-1 , 1-110 and 1032 Writing these in the form of linear combination x* 110-1 +…

Q: 1 0 Find characteristic equations of the matrix A = 0 1 λ+2λ-1 = 0 1. O λ-2λ-1=0, 2. О 2²+22 +1= 0…

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Q: 2 1 -2 Suppose that a 3 × 3 matrix A has det A = 1 and that its cofactor matrix is C = 1 1 -2 -1 0…

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Q: 5. Let A -1 2 1. Express the matrice A as the product of elementary matrices. 3 1

A: We have to express the matrix as the product of elementary matrices.

Q: Find the characteristic equation of the matrix by inspection. [6 -5 4 7] 0 -5 0 0 3 0 LO 0 8] = 0…

A: The characteristics values of a diagonal matrix are its diagonal values itself.

Q: [O 1 0 If A =0 0 1 then show that, A = pl + qA + rA where I is the identity matrix of order 3. %3D…

A: The given matrix is A=010001pqr To prove A3=pI+qA+rA2

Q: QUESTION 6 For which value(s) of a will the matrix O 2a A = a+2 1 be orthogonally diagonalizable?…

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Q: -42 -36 Let A= and let B = 33 15 Solve the matrix equation for X : 3X = 3A – B. %3D

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Q: [1 2 1] A = 2 0 2 l2 3 kl give matrix. [A| = 1 , k=?

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Q: 2. H -1. Use the matrix formed by {₁, 2, V3} to 5 determine whether the {₁, 2, 3} spans R3. Explain…

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Q: 시(3)-() 2 Find the matrix A satisfying A !3! and A and write the SVD of A in vector form. [Hint:…

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Q: 1 1 11. Let A = 1 -1 1 Find an orthogonal matrix U E R³×3 and diagonal matrix D 1 such that U AU =…

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Q: Question No. 2: Verify that the following matrix is an Orthogonal Matrix: cosø sinø sin Osinø cos 0…

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Q: 2 1 1 1 2 1 0 0 1 Jse Cayley-Hamilton theorem to find A20 where the matrix A =

A: A=211121001A-λI = 2-λ1112-λ1001-λ…

Q: [ -2 2 Let A = 2 i Find a matrix P that orthogonally diagonalizes A. Then, verify that 1 the…

A: Given that,A=-2221The matrix P that orthogonally diagonalizes A is determined as shown below.

Q: QUESTION 3 For what value of k (upto one decimal place), the vectors u= (9,-9), v=(7,k) are linearly…

A: 4.we have apply operation of given matrix 3. For what value u and v us linearly dependent If…

Q: Question No. 2: Verify that the following matrix is an Orthogonal Matrix: cos ø sinø cos 0 -sin 0cos…

A: 2-Given- cosϕ0sinϕsinθsinϕcosθ-sinθcosϕ-cosθsinϕsinθcosθcosϕ To Prove- That the above matrix is…

Q: Question 5. Let U be a unitary matrix. Prove that || Ux ||=|| x || for all columns x e C". Hint.…

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Q: (1 2 2 1 2 2 b) Let A =| 0 -2 0and B =| 0 1 Find the elementary matrices E,, E,,E, to multiply A, to…

A: We have to find Row Elementary operations to get Matrix A from Matrix B.

Q: Г2 3 1 1 Let A = and B= . Find the (1,1)-entry of matrix X given 1 3 5 that AX+A=B. O5 O1 2.

A: Solution: The objective is to find the (1,1)-entry of matrix X

Q: 5. Let A = (, ) nd z- (). 1 and a Consider the matrix equation Ag = ka where k E R. Then the scalar…

A:

Q: Question 3 s): Let -1 A = 3 -9-18 7 (a) -, Find the cofactors: A1, A21, and A31 (b) ( - Find det(A)…

A: We have to find the cofactors and det(A).

Q: Question 2. Let P be an orthogonal matrix. (a) Prove that det P = 1 or det P = -1. (b) If det P =…

A: Orthogonal matrix: A square matrix Ais said to be orthogonal if  AAT=I, where I is the identity…

Q: - Let 3 -2 0] 6,B 3. -2 A : 1 -3 7 12 -2 1 -2 1 a. Find the elementary matrix E such that B = EA. b.…

A: NOTE: Refresh your page if you can't see any equations. . . so the elementary matrix is

Q: If A is any square matrix. Then det(A) = a) det(A-1) b) det(AT) c) – det(AT) d) 0

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Q: [1 0 0 41 250 3 3 00 2 L4 3 2 1 ) Let, A = be a 4x4 matrix. Find det (A) and det (2ATA).

A: To find |A|   Also to find |2AT A|

Q: I. State whether or not the given matrix is (a) upper triangular, (b) lower triangular, (c)…

A: To state whether or not the given matrix is a) upper triangular b) lower triangular c) diagonal d)…

Q: (a) Show that the matrix P is regular. (b) If x(0) = (1,0) what is x(1)? (c) Show that vị = (1, 1)…

A: A Stochastic matrix is also a regular matrix . If has only non-zero positive entries.

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: Question 2 Let T: V → V be a linear operator where dim V = n. Let a = (v1,.…., Vn) be a basis of V.…

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Q: Question 3: Solve the second-order equation d²u u(0) = || : u' (0) и, dt2 1 Question 4: Show that…

A: Using laplace transform

Q: Find the characteristic equation of the matrix by inspection. -2 5 27 -1 0 0 0 80 0 0 4 The…

A: Given matrix is 4-2520-10000800004

Q: Question 1. Is the matrix A is Hermitian, where A- (2, ':') A = Yes No 1- i 0 1 0 1 2 0 0 0 A = Yes…

A:

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.