Answered: [O 1 0 If A =0 0 1 then show that, A =…

Math

Advanced Math

[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 Pqr

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.3: Symmetric Matrices And Orthogonal Diagonalization

Problem 60E: Find ATA and AAT for the matrix below. What do you observe? A=[132461]

See similar textbooks

Related questions

Q: Let [1 2 [1 A = 2 41 1 3 and B = |2 1 [2 2 6] 2 4] 3 [1 2] Find the elementary matrix, E such that…

A: Two matrices A=124213102 and B=124213226 are given. We have to calculate the matrix E that satisfies…

Q: 1 0 0 If [B|I]=| 0 1 where I is the Identity matrix then B¯1 0 0 1 OA. OB. OC. Does not exist. 1,…

A: Answer is option A)

Q: Find an example that meets the given specifications. 3 x 3 matrices A and B such that AB ± BA 0 0 0…

Q: Consider the following matrix 3 A = 1 1 4 -1 1 a) Show that the matrix A is positive definite. b)…

A: a) A = AT This is a symmetric matrix because that's is equal to its…

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

Q: Q2: Let A, B be matrices of size 3x3 such that and AB = A+2I A = -101 21 2 find A, B?

Q: find DA and AD, if possible, where D = D,(3,0, 2, – 1) and A is the given %3D matrix. 21 1 31 0 1+i…

A: Given: D=Dg3,0,2,−1=302−1, and A=2i013i01+i80−i10i1111 To find DA and AD if possible.

Q: Which of the following is an elementary matrix, E, such that EA= B for 1 %3D 1 0 1 A = 2 2 and B = 1…

Q: For a, b, c € R, suppose that A is the matrix a + ib A= 1 = (1/√² 17/12). 1/√2) (a) For what values…

A: Given matrix is A=ca+bii/212 Solution a: i- Hermitian: For Hermitian matrix A=AT Also aij=aji Its…

Q: Find a matrix B such that AB = I, where 6 1 A = 1 0 0 1 and I = -6 6 a b Hint: Let B =c d

Q: Consider M = | 0 2 0 . Use the Cayley Hamilton theorem to find (M +4I)-1 where %3D 2 0 1 I is the 3…

Q: 10. Let A E R"Xn be an upper triangular matrix, and let B = A¡j for some i, j. (a) (BH) Show that if…

A: Upper triangular matrix: A matrix of order n×n is said to be upper triangular matrix if each element…

Q: (e) Find all possible values of c for which the following matrix 1 1 1 F = c 9 1 3 1 is singular.

Q: If A is n x n matrix and a E N (AT A), then a. IEN (AT) O b. r b. IEC (A") Oc. rEC(A) O d. rEN(A)

Q: (b) Let A, BE G Le(Z1) with I the identity (unity) of a 6 x 6 matrices. Prove that if AB = I then BA…

Q: snip

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

Q: [3 2 07 ) Let A= 1 0. Show that A +10 I = 7A, where I is the identity matrix of order 3 0 0 5

A: See the attachment

Q: Find elementary matrices e and e2 such that di 0 e2 = 1 5 1 5 e1 0 dz) for some numbers d and d2.

Q: If G = X| is alx1 matrix, and A is a 1xn matrix, is it true that XA = GA for an)- any number A. Is…

Q: [0 1 01 [1 1 0] = 0 1 li 1 MR, = |1 0 1and MR, Lo 1 ol Find the matrix representation of R2 • R1.

A: R1 =010101010 and R2 = 110010110R1∘R2 = ?

Q: o 1 0] If A=|0 0 1 then show that, A = pI +qA+rA² where I is the identity matrix of order 3. p q r

A: For a square matrix A of order n |A−λI|=(−1)n[λn+a1λn−1+a2λn−2+...+an] and the characteristic…

Q: 1. Let x E C" and y E C™, with y # 0. Consider the m x n matrix defined by A = yx*. (a) Show that…

A: Given that x∈ℂn and y∈ℂn, with y≠0. Consider m×n matrix defined by A=yx*. To prove (a), (b) and…

Q: Jump to level1 (E)-E (:). {} H} 2x2 4 B = x1 Let T : R² → R² be defined by T . Let u = and x2 2x1 –…

A: Step:-1 According to Fundamental Theorem of Matrix Representation:- TBC PB u =PC Tu, ∀u∈ℝ2…

Q: A = [aij]nxn 0 ; i – j| = 1 ise 1; i– j| # 1 ise Which of the following is a matrix A written…

Q: Use the elementary matrix E to find E A using an elementary row operation. [1 0 0 8 E = A = 1 0 0 0…

A: To find EA

Q: 1 a b a,b,c e R including A = 0 10 0 0 100 Let the matrix be given. According to this,

Q: Consider the following two elementary matrices. 1. E1 - E2 = Suppose that A is a 2 × 2 matrix such…

Q: Which of the following is/are not an identity matrix? [1], в %3 1 B = 1 0 0 D 1 A C 0 1 1 0 0 0 1 0…

A: The identity matrix of size n is the n × n square matrix with ones on the main diagonal and all the…

Q: Q1. Use Cayley-Hamilton to calculate eAt for the following matrix: 1. -1 1 -1 1

A: Matrix 1-1001-1001 To find : eAt by using Cayley hamilton theorem.

Q: Find the elementary matrix E such that EB = A where %3D 2 1 1 24 1 A = 4 --2 and B -12 -8 3 6. -8 3…

A: We will find the elementary matrix.

Q: 1 1 Given that y -1 is the cofactor matrix of E = 0 w -1 1 2 -1 Find the values of a, y, z, and w.…

Q: 3. Let A be n x n matrix that has zeros on the main diagonal and ones everywhere else. Example of a…

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

Q: -1 7. (S.15). Verify that the matrix A = 0. is diagonalizable; 4 8, (S.10), Let H is a dot nuo 005…

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: Which of the following is false? O A- = 4 %3D O AC is the adjoint of matrix A O Al = IA = A where I…

A: topic - matrix

Q: Question 5. Show that every matrix X e Mnn has the form X = A" – 2A for some matrix A E Mnn· Hint:…

A: Given problem is:

Q: (iv) Given the matrices 3 1/3 -1/6 and B =D 1/2 A =0 Verify that AB BA = I where I is the identity…

A: Given that A=3102 and B=13-16012 verify AB=BA=I

Q: 1 0 1 3 0 2 6. Let A = and B = %3D 5 1 (a) Calculate the matrix Aª.

A: given matrix A=1051 (a') to find A4 multiply the matrices using matrix multiplication. A4=A2·A2…

Q: Find an example that meets the given specifications. 3 x 3 matrices A and B such that AB ± BA 0 0 0…

Q: Let A and B be 0 1 -3 1 2 A = 1 2 B = 0 1 -3 2 2 -1 2 2 -1 | Find an elementary matrix E such that…

A: When we perform a single row operation on this identity matrix we get a matrix known as the…

Q: * (E)- ---{}-}- -2xı + 2x2 Let T : R? → R² be defined by T , and Let u = %3D 3x1 – 3x2 C = -1 use…

Q: Let -6 1 -2 4 1 3 0 3 5 -1 т -2 L4 0 1 -1- Find the value of m, if C41 = -12, where Cj is the…

Q: that АВ I I со X Y Z O Find formulas for X, Y and Z in terms of A, B an C. It may be necessary to…

Q: -4 Let A = Find a matrix B such that AB=I. 1 - 1 1 O a) 4 O b) 1 1 4 3. c) - 3. 3 1 4 3. o d) 3. 4…

A: To find a matrix B such that AB=I

Q: Find the elementary matrix E such that EC = A where %3D 4 4 A = |3 -1 and C = 3 0. -1 9 -8 19 0 4 ?…

Q: 0 0 What would the answer be for Ax = b if A = L|0! 0 U? The %3D %3D 0 0 matrices L, U and b are as…

A: Given that A=L160001500013U, Where L=100−1100−11 and U=1−1001−1001 We have solve the equation Ax=b…

Q: 1 0 2 0 2 0 20 1 I is the 3 x 3 identity matrix, working over Z5. 13. Consider M : Use the Cayley…

Q: 4. Let u E R". Can you find a matrix A E Mmæn (R) so that Au = u for all u ER"?

A: For the solution follow the next step.

Question

0 1 0
4. If A= 0 0 1 then show that, A = pl + qA + rA where I is the identity matrix of order 3.
%3D
[P qr]

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Matrix Factorization$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Let A,D, and P be nn matrices satisfying AP=PD. Assume that P is nonsingular and solve this for A. Must it be true that A=D?
Which of the following operations can we perform for a matrix A of any dimension? (i) A+A (ii) 2A (iii) AA
Find ATA and AAT for the matrix below. What do you observe? A=[132461]
For what values of a does the matrix A=[01a1] have the characteristics below? a A has eigenvalue of multiplicity 2. b A has 1 and 2 as eigenvalues. c A has real eigenvalues.
Prove part b of Theorem 1.35. Theorem 1.35 Special Properties of Let be an arbitrary matrix over. With as defined in the preceding paragraph,
Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and nullity of AB. b Show that matrices A and B must be identical.