2 2 [1) Let A Does there exist an invertible matrix P such that P-AP 1 %3| 3 3

Q: -1 Find all values of x such that the matrix 8 is not invertible.

A: A matrix is invertible, if the determinant of the matrix is not equal to 0 . Suppose a matrix B is…

Q: 3 0 Find a matrix P such that P- 30 2 1 1 0 O A. P= 1 1 - -1 0 O B. P 1 1 1 -1 C.P = 0 1 1 0 O D.P 1…

A: P-13021P=3001 From the given that P-1AP is diagonal matrix A=3021 We need to find the eigenvectors…

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: 7. Suppose that A is an invertible matrix and AB = I, Then (a) Show that BA = I, and (b) And the…

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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

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Q: Find an invertible matrix P such that: 2 -2 1 P-1 -1 3 -1 P 100 2 -4 3. 0 0 6

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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: Find values of a for which the following matrix is not invertible: 1 a+ a 2

A: 1a+1a-24

Q: 2. (a) Let J= [28]. Show that there is no matrix X such that X² = J but that there are infinitely…

A: Matrix properties are used

Q: -48 Find an invertible matrix P and a diagonal matrix D such that D = P 'AP. 10 4 Let A 24 10 -96 0…

A: Given: A=-104-48-2410-96002 Characteristic equation of matrix A is given by A-λI=0…

Q: 4. Determine all values of p such that the matrix A is invertible. 1 р 2 A = р 3 4 1 1 -2

A: The condition for a matrix is to invertible is its determinant must not be zero. We should find the…

Q: **15. Suppose A is an m × n matrix and x e R" satisfies (AA)x = 0. Prove that Ax = 0. (Hint: What is…

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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: (1) Let A Does there exist an invertible matrix P such that P-AP = 3 (2 0` 0 3

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Q: find value/values of k such that matrix is singular 10 3 2 -1 0 4 2 k

A: We need to find k such that the matrix 1032-1042k is singular. So, we must have,…

Q: 5. An LP is said to be self-dual if it is equivalent to its dual. a. Construct an instance of a…

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Q: The Matrix A =| -1 2 is not invertible. 0 1 O True O False

A: Given: Matrix A is given as follows: A=-1201   Invertible matrix definition: A matrix is said to be…

Q: 3. Write an example of matrices B, A such that A is k x n and B is n x k for some positive integers…

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

Q: 4. Let A be a 3 x 4 matrix and B be a 4 x 5 matrix such that ABx = 0 for all x E R°. a. Show that…

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Q: -4 9. 15 Show that A = -1 1 and B = 3 are similar matrices by finding an invertible matrix P…

A: A matrix A is similar to another matrix B when their determinant is the same, their characteristic…

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: The matrix 1 0 1 -1 1 1 1 0 1 [ −1 1 1] has no QR factorization. O True O False

A: We have to determine the following statement is true or false ; The matrix  101-111101-111  has no…

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: Q3. Let A be an n x n positive definite and symmetric matrix, and X an n × n invertible matrix. Show…

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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: [11 25 Let A a Find an invertible matrix P and a matrix of the form C = a with the property that A =…

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Q: Let -3 -1 2 - A = 1 -1 -4 -1 3 Find an invertible matrix P and a diagonal matrix D such that D =…

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Q: a *15. Given a = 6ER°, define T: R³ → R³ by T (x) = a x x. Prove that T is a linear trans- formation…

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

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

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Q: A is akxl matrix with rank r and nullity n. If 2r + n = 10 which of the following cannot be the…

A: it is an application of rank nullity theorem.

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: 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: Find the values of k for which the matrix A is invertible. k – 3 -2 (а) А— -2 k 2 1 2 4 3 1 6 k 3 2…

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Q: -5 -8 Show that the matrix A = 0 is involutory. 1 -1 3.

A: Definition of Involutory matrix: Let A be a Square matrix, A is involutory if its inverse is same as…

Q: 1) Suppose that T is a linear operator with standard matrix 8 3 6 0 2 0 0 7 Is T one-to-one?…

A: Given the linear operator T:ℝ3→ℝ3 836025007 Now, we find determent of T.…

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

A: Let A=10k010001 To show that A is similar to the orthogonal matrix iff k=0: i)To prove k=0: Let A be…

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…

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Q: (b) Write down an invertible matrix P such that [o 0 -21 P-11 2 li 0 [2 0 0] 1 P = 0 20 lo o 1 3 P=…

A: 1)

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…

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Q: (3) Consider the matrix [1 k 31 A = 2 4 -6 2 For what values of k is A invertible?

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Q: 3.9. Let a matrix B is [1 -21 B = 13 Find B6 by using a nonsingular matrix P such that D = P¯'BP is…

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Q: Let A be the matrix 7 1 Find p(A). p(x) = x - 2x + 4

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Q: 3 5. Suppose that A is an invertible matrix with A-1 a. Find A.

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Q: Let 1 0 8 5 A = 4 7 В 0 -2 C = %3D 5 3 5 0 -3 3 2 -1 Find a matrix X such that AXB = C.

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Q: Write an invertible matrix P such that 3 0 0 p-1AP '=|0 -1 0 0 -1 0 0 4

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Q: 30 30 Find a matrix P such that P= 2 1 1 -1 P = O A. -1 0 P = O B. OC. 1 1 1 1 O D. 0 1

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