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

Q: 7- Which of the following statements is FALSE? 1 2 0 a) The matrix A = 0 1 0 is in reduced echelon…

A: Elementary matrix :- An elementary matrix is a square matrix that has been obtained by performing an…

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Q: 5. Let 2 0 A= H 2 2 0 -3 0 - find the matrix noms

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Q: [1 1 1] Suppose we have a matrix A= |1 0 1 2 1 2 What is rank of A?

A: GivenA=111101212R2→R2-R1R3→R3-2R1A~1110-100-10R3→R3-R2A~1110-10000We know that The rank of a matrix…

Q: 4. Assume the invertible matrix A satisfies 10 4 2 1 3 1 1 A 4 A -1 -1 A 6 1 -2 3 4 -3 Find the…

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Q: -x-1 -x 2 Let A = 1 2 (i) Determine an expression for det(A). (ii) For what values of x will the…

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Q: -3 If A is 3 x3 matrix such that A 1 -3 then A is 4 diagonalizable. Select one: True False

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Q: 2 1 -1 4 previous problem to determine a matrix S such that Show that A is defective and use the 3…

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Q: 5. Find all values of 2 for which the matrix 2-3 0 5 0 2+2 0 S 0 is singular. 215

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Q: 13.) Determine the matrix: s P 6-8 3 ។ -3 the dimension X 10

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Q: A. Find the determonant of the matrix A 1 2 1 -21 -1 -2 -1 4 2 1 3 2 -2 1 2 -3

A: Given :A=121-2-1-2-142132-212-3

Q: 2 – 1 Find the values of a for which the matrix A = 2– 2 1 is invertible. 2

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Q: 5. Consider the 3 × 2 matrix A such that 3 A and A 5 3 (a) Write down A. (b) Is A singular? Justify…

A: For the given information, we have to answer the following...

Q: -1 Find the rank and nullity (i.e. dim col A and dim null A) of the matrix A = 2 -4 1 11 - 12 2.

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Q: -4 8. find the inyerse of the matrix ら -4 12 by Gaussian Jordan eliminaton methed

A: Given, a-48-412b6-c21100010001 Now take, R1→R14,R2→R24,R3→R33 Then, a4-12-13b42-c37140001400013

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: -2 Find the matrix P such that P-'AP is diagonal matrix. -2 (c) Let A -2 3 -1 -1 3 6.

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Q: 3 5. Suppose that A is an invertible matrix with A-1 = a. Find A. b. Find the 2 x 2 matrix X so that…

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Q: It exists, Ol the matrix. 1 - 1 2 – 1 1 1 1 2

A: A-1=?

Q: -5 2 -2 Show that A E 3 -2 -2 and B 1 -4 are similar matrices by finding an invertible matrix P…

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Q: (b) The rank of the matrix A is 2. (2 4 2 A =1 k 3 1 2 2/ (1) (ii) For this value of k, is A…

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

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Q: 4 8 -12 A--16 -32 49 20 40 -55 Express A in the form A LDU, where L, is lower triangular with 1's…

A: Lower triangular matrix: A square matrix in which all the elements above principal diagonal are zero…

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

A: Matrix multiplication, for matrix A and B can only be done if the number of columns of A is equal to…

Q: (4) For what values of z is the matrix A invertible? (5) Solve the system of equations in part (2)…

A: The given linear system is  Axy=b where A=0.10.60.5z and  b=1811 Solution (4) Matrix A is invertible…

Q: -1 1 Verify that the matrix A = 3 is diagonalizable; 4 -2 5

A: We will use condition for matrix to be diagonalizable

Q: 1. Show that matrix A is singular 1 2 A= 3 -1 -2 3 -2

A: Given  A=1203-12-23-2

Q: Let 4= [ 12 -0,²5] 3 Find an invertible matrix S and a diagonal matrix D such that S-¹ AS = D.

A:

Q: 1 0 4 if A= 0 2 3 1 -3/ Find: www The rank of matrix A* O 2 O 3

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: -3 6. ). Find all a so that the matrix A= -1 1 2 is positive 1 defined:

A: We use the following result to find the alphas. Result: An n*n matrix A is positive definite iff all…

Q: 0 2 1 2 4. Find the rank of the matrix N = 2 10 1 201 4

A: We have been given the matrix  Note - Since you have posted with multiple questions so, we will do…

Q: 5.- Let the matrix [A] be given below, obtain its corresponding matrix of cofactors. 3 -2 4 [A] =…

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Q: 4. If A is 4x4 normally distributed random matrix and I is 4x4 identity matrix. Proof that: a) A'A =…

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Q: 5. Consider the matrix 11 -5 A = -2 10 (a) Compute the singular values for A (b) Compute the SVD for…

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Q: (b) The rank of the matrix A is 2. 2 4 2) A = (1 k 3 1 2 2/ (i) (ii) Determine the value of the…

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Q: 4: Let 6. A = | 0 7 0 0 7 (a) Find a matrix P that diagonalizes A. (b) Find PAP [using your answer…

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Q: (b) The rank of the matrix A is 2. 2 4 2 A =1 k 3 \1 2 2 Determine the value of the constant k. (i)…

A: Matrix rank and inverse of the Matrix, if Matrix is singular then Matrix doesn't have invese

Q: 3. Let A be an invertible matrix such that A-¹ = NOT 2 0 1 2 01 1 1 Solve the system (2A2)x= b,…

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Q: 5. Find the cofactors and the adjoint matrix of A where (1 1 -1 b) A =|2 3 7 0 -1 a) A =-2 0 -2 4 -3…

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Q: 5 2 2 5 Let A= 3 -1 B = 4 7 4 3 8 Find the matrix D such that CD - AB= 0

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Q: A 10 x 16 matrix A has maximal rank. What is its nullity? а. 26 b. 16 с. 10 d. 6 е. О

A: Using Rank- Nullity Thereom,

Q: 5. Identify an elementary matrix E such that 1. E- 2 2 4.

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Q: (1 3 4 Q3: LET A = ( 3 0 4 1 2 -1 1- find |A|. 2- Determine if A symmetric matrix or not ? why ?

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Q: 5 -2 1 1 Show that A and B are similar matrices by finding an invertible matrix P satisfying A = P…

A: As this problem is related similar matrix, hope you know how to find inverse of a matrix,…

Q: -11 is singular -3] a Q1/A) Find the value of a, where A = 3 -1 -2 a matrix.

A: Since you have asked multiple questions in a single request we would be answering only the first…

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

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Q: а 3 2 Find the value of a that make the matrix A 1 2 3 3 1 2 - singular. a =

A: A matrix will be singular if value of its determinant is zero  => If A is singular then A=0

Q: 5 15. Let A be the matrix -3 1 (a) Compute A-!. (b) Use part (a) to find the unique solution to the…

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Q: (7) (I Let A? = I be an n x n matrix and A# 1. Show that A is diagonalizable.

A: