1 0 k Q11. Show that the matrix | 0 1 0 is similar to an 00 1 orthogonal matrix if and only if k = 0.

Q: (iv). Find det(A¯1) of the following matrix: 1 3 -1 2 1

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Q: Find a 3 x 3 matrix A such that Ax = 9x for all x in R3. A II

A:

Q: Find the elementary matrix E such that EB = A where %3D 5 4 1 ] 4 1 A = |4 |7 -6 1 -1 and B = |12 3…

A: EB=A multiplying with B-1 on both sidesEBB-1=AB-1E=AB-1

Q: 1 Suppose that a 3 x 3 matrix A has det A = 1 and that its cofactor matrix is C = 1 2 |-7 4 2 Find…

A: Formula: Let A be a n×n matrix with non zero determinant then, A-1=1det ACT where C is the cofactor…

Q: 2. Let n x n matrix A have the form Au Azz A = where An is k x k (where k < n). Show that A is…

A: The given matrix is  A1100A22 A matrix is called non-sigular if the value of its determinant is…

Q: Find an invertible matrix P and a diagonal matrix D such that PAP=D. 1 3 A = | 0 -5 -6 0 3 4 0 0 0 0…

A: NOTE: Refresh your page if you can't see any equations. .

Q: Given the matrix 3 1 0 -3 0 1 -1 A = 1 1 2 2 1 -1 3 Find an invertible matrix P so that J = P-1 AP…

A:

Q: [1 2] Find a matrix X such that AXB = C, where A = 2 1 0 0 [2 0 B and 0 1 1 1 C = 0 1 -1

A: For multiplication of the two matrices there is a condition which says Number of column of first…

Q: 1 1 Given that matrix P=|1 0 |0 -1 2 1 , find the matrix A such that -2 0 0 P'AP=| 0 -2 0 0 4

A:

Q: Show that the matrix X -1 : -1 -1 X : 0 : : X is Positive Definite if x > √n −1 The lower right…

A: The given matrix is An=x-1...-1-1x00::⋱:-100x. To Prove: This matrix is positive definite if…

Q: Q3. Consider the matrix -1 A = -1 1 Compute || A||2 using the SVD of A.

A:

Q: (4) Let A E R™xn be any matrix. Solve the following problem min ||AX – I||r Hint: Write X = [x1,...,…

A:

Q: V2 1 2 11 T = 0- 2 000 -Vī

A: If A is a matrix of order and I is the identity matrix of order, then If A-1 is the inverse matrix…

Q: 2. (a) Suppose (B − C)D = 0, where B and C are m x n matrices and D is invertible. Show that B = C.…

A: Explanation of the answer is as follows

Q: 3. Find the matrix X, such that XC - 2C = DXC satisfies. 3 4 4 4 1 C = 1 2 1 D = 1 0-2 4 1 -1 -3

A: Since there are multiple questions, we are solving the first question. Please post the questions…

Q: 5. Let D be a non-singular matrix such that 7. (7D)- 1 -2 Find D.

A: Inverse matrices

Q: Let -1 A = 1 0. 15 -2 (5a) Find a 3 x 3 matrix P and a diagonal matrix D = such that A PDP-1 (5b)…

A:

Q: 5. Let A be an n x n matrix. Show that if B = S-¹AS for some nonsingular matrix S, then det(B) =…

A: Here, given that: B=S-1AS

Q: 7 Show that A = 13 and B = 4 2 are similar matrices by finding an invertible matrix P satisfying 2 A…

A: Given,A=7-132-4 abd B=1-2-22Let,P=abcd , and P=ad-bc=nSo, P-1=1nd-b-ca where n=ad-bc=dn-bn-cnan

Q: Which of the following matrices is a nilpotent matrix of degree 2. a a) where ab =-x². -x a where ab…

A: We have to select the nilpotent matrices of order 2 from the above list.

Q: 1. Find an example of a 2 x 2 matrix A such that A² # I2, A³ + I2, and A® = I2. Explain how you…

A: Given that  a 2×2 matrix A such that A2≠I2,  A3≠I2 and  A6=I2

Q: 1 a Consider a 3x3 matrix P= 0 1 2, and an another matrix 0 0 1| Q = [q] such that P² -Q =I.Here, I…

A: Given a 3x3 matrix P=12a012001, to find a 3x3 matrix Q such that P2-Q=I, where q13=8, that is, the…

Q: 7. For a matrix B= 1 0 0 1 -1 0 5-1 -3 find B¹ by using the Cayley-Hamilton theorem.

A:

Q: Let A and B be -1 0 10-3 A = 10-3 -1 0 2 1 2 1 2 2 Find an elementary matrix E such that EB = A.

A: Given that: A=-10210-3122B=10-3-102122

Q: 1 2 1 Find a matrix Z such that D=Z AZ is diagonal, if A -2 1 3

A: The matrix given is as follows: A=1-21-25313-2 First, we will find the eigenvalues of the given…

Q: 5. Find if possible a nonsingular matrix P such that P'AP is diagonal. [1 2 a. A= b. A= 4 -8 -8

A: Given matrix  a.) A=122-1 b.)A=74-44-8-1-4-8-1 To find possible a non singular matrix P

Q: Find the value of k so that matrix A singular. 1 1 1 -k A = 3 2 -6 -2 2k O 1 3 O None of the above

A: topic- matrices and determinant

Q: ?) A is an n x n matrix, such that 2A3 – 4A? + 6A – 21 = 0 (where I is the identity matrix and 0 is…

A:

Q: 4. Express the following matrix A and its inverse (A-1) as products of elementary matrices, 1\ A =…

A:

Q: Find an invertible matrix P and a diagonal matrix D such that PAP-D. -6-3 9 A = 5 2 -5 -3 -3 6 3x3…

A: For this problem, first we will find out the eigenvalues of A and corresponding eigenvectors. Then…

Q: Find an invertible matrix P and a diagonal matrix D such that PAP=D. 0 0 A= 30 -2 -10 -2 -15 0 000…

A: Solution:

Q: 2. Find the values of k for which the matrix B is invertible. -2 B= 0 k 1 3 2 1 4 -1

A:

Q: If A and B are square matrices of the same size such that det (A) = det(B), then det(A+ B) =…

A:

Q: ^ = [1 ] A If A is diagonalizable, find an invertible 2 x 2 matrix P and a 2 x 2 diagonal matrix D…

A: Given that the matrix A=0-440. If the given matrix is diagonalizable , find an invertible matrix and…

Q: (-1 2 (b) Compute p(A) for the given matrix A = and the polynomial p(x)=x² – 2x+1 0 3

A:

Q: Given the matrix -3 -1 1 4 1 -2 1 A = 3 -3 1 -2 -1 0 -3| Find an invertible matrix P so that J =…

A:

Q: Find the values of k for which the matrix B is invertible. B = -2 1 0 2 k 4 3 1

A: We need to determine the values of k for which the matrix: B is invertible.

Q: Suppose A is a 2 × 2 matrix, where -2 | u = Au = -4 A?u = 4 A³u 2 20 – 20 – 10. The minimal…

A:

Q: [1 Find a matrix A = -4 -51 = l3. y] 1 z such that A² 10 %3D Lo 1. Lo

A: Given A=1xy01z001 A2-0-4-50010000=I3 To find Matrix A:

Q: The matrix V3 1 A 13 is an orthogonal matrix. True False N]- N

A:

Q: 3. If A is a nonsingular matrix, then A' is nonsingular and its inverse is (A')1 = (A') '. Prove it!

A: A matrix A is said to be invertible if and only if  det(A) is not equal to zero i.e.  |A| ≠ 0

Q: If A? is a zero matrix, then AT A = 0 is: %3D O a. Not possible unless A is a zero matrix O b. not…

A:

Q: Find k for which the matrix below is NOT invertible. 1 1 3 -1 2 1 k

A: For matrix to be non-invertible, it's determinant must be 0. We will use this property to find the…

Q: q4: If  det(A) =|A|= 0, then A is called a non-singular matrix  True  False

A: Non-Singular matrix: A non-singular matrix is a square matrix whose determinant is not equal to zero…

Q: Let A = 0 D = P-¹AP. P = -2 -21 -1 Find an invertible matrix P and a diagonal matrix D such that 0…

A:

Q: Let -[ -1 7 1 0 -1 A= 15 -2 (a) Find a 3 x 3 matrix P and a diagonal matrix 0 0 D= | 0 0 0 Ag such…

A:

Q: Suppose A, B, and X are invertible 3 x 3 matrices. Suppose that [1 2 0 0 1 1 1 3 • A8 = I3; and…

A:

Q: T 4.4-10 Show that Choleski's method is applicable whenever the matrix A is of the form BB with B an…

A:

Q: [3 Decide whether the matrix A = 0 -3 0 is diagonalizable. If so, find P such that P-1AP L5 is…

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Q: 2. Let A be a 3× 5 matrix such that A = [1 2 ūz v4 05), where ī1, i2, 03, 04, ūz E R³, and Find ūz…

A: We have to solve given problem: