1 3 (b) If possible, express A = 2 3 product of elementary matrices.. as a

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: Express A as the product of elementary matrices where A = 3     4        2     1

A: Solution Given A=3421We need to find the product of elementary matrices

Q: Let 1 1 0 20 2 A 1 1 (a) (Ъ) you have used in (a); Compute A-1; Find the elementary matrix…

A: For part a: The objective is to find the inverse of the given matrix A=110202011

Q: [-1 0 0' 0 1 1 if possible. Show all your work. 1 1 Diagonalize the matrix A =

A: Given: A=-100011011 To find: Diagonalize matrix.

Q: 0 2 4 1 2 3 259 a) Express A = as a product of elementary matrices.

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

Q: 1 2 3 1 A = 1 0 1 -1 2 1 1 Find rank of the matrix

A: We have to find the rank of the given matrix…

Q: 4. Let A, B, and C be n-by-n invertible matrices. Then (ABC)- is equal to O A 'B'C! O A-ªC-'B-!…

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Q: Express A and A-1 as a product of elementary matrices. 0 5] A = 0 1 6 1 0 3] [1 0 5] 0 31

A: Here in the given question matrix A is given and objective is to express A and A-1 as  a product of…

Q: TRUE/FALSE If A is nonsingular, then A can be factored into a product of elementary matrices.

A: Given: The statement is “ If A is non-singular, then A can be factored into a product of elementary…

Q: 1 0 0 0 1 5 -10 1 0 2 1 0 0 Diagonalize the matrix A : if possible. 3

A:

Q: 13. Find matrices A so that a. A +0, but A² = 0 b. A? + 0, but A³ = O Can you make a conjecture…

A: First we will find matrix which for each case a. and b. then we will try to make a conjecture on the…

Q: 18. True or false? Let A, B be two 3-by-3 matrices with real entries. If det(A · B) = 0, then A-1…

A:

Q: 3. Show that A and B are not similar matrices. [1 2 0 A = 0 1 -1.B [2 1 11 ,B= 0 1 0

A: # as per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: 3. On the basis of the matrices given in Example 9, is the product BA defined? If so, calculate the…

A: Matrix multiplication: Let us consider two matrix A and B  of order m x n and p x q  then the matrix…

Q: Q3: Express A and A' as a product of elementary matrices. [10 5] A = 0 1 11 6 0 31

A: Given matrix is A=100010-101

Q: 1. Show that the matrix 2 1 A = 1 2 -1 -1 is positive definite.

A: Given :- a matrix A  We need to show that a matrix is positive definite. We know that , A symmetric…

Q: Express A and A- as a product of elementary matrices. [1 0 51 A = 0 16 li 0 3

A:

Q: Let A, B, and C be invertible matrices. Then (4BT A-1C²)-1 is equal to None of the mentioned equal…

A:

Q: Q3: Express A and A-1 as a product of elementary matrices. [1 0 5] A = 0 1 6 li o 3]

A:

Q: 3. The following matrices are elementary matrices except (a) 1 0 1 0 (b) 5 1 (3 (c) 1 (d) -3 -

A:

Q: 1. Find an example of a 2 x 2 matrix A such that A? + I2, A3 + I2, and A6 = I2. Explain how you…

A: Given A3≠I2,A2≠I2and A6=I2

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

A:

Q: 5. Let A= (a) Find the inverse of A, and (b) Express A as a product of elementary matrices,

A: Elementary matrices: Let E(k×i+j) denote the elementary matrix obtained from identity matrix I by…

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: 3: Express A and A-1 as a product of elementary matrices [1 0 51 A = 0 1 6 li 0 3] 1

A:

Q: Let A, B be 4 x 4 matrices. Find two matrices so that rank(A) = rank(B) = 2 and rank(AB) = 1. A = B…

A:

Q: Example 1: For the matrices A = 0. and B= compute AB andA-1 and B-1 and (AB)-1.

A:

Q: |2 0 if A=| -3 -2 4 and B= 1 find the Matrix X such that 3A+4X=5B 1 3

A:

Q: .

A: Given : A2164* Express A-1 as product  of elementary matrices * Expresss A as product of…

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: If A + 0 and B+ 0 are square matrices of the same order, then AB + 0.

A:

Q: 2) Find inverse matrix using Gauss Jordan Method if available 2) [3 2 -1 A = |6 2 15 0 1

A:

Q: By simple observation find the product of the three matrices. Explain. 0] [1 1 0 0 0 0 0 0 [ 2 0 1 3…

A: The matrix multiplication is possible only if the number of columns of the first matrix is equal to…

Q: 27. Find examples of (2 × 2) matrices A and B such that det (A + B) + det(A) + det(B).

A:

Q: 1. Are the following matrices diagonalisable? Explain your answer. 2 0 50 1] a) A =-2 3 -1 -2 0 3 c)…

A: A matrix is diagonalizable if and only if for each eigenvalue the dimension of the eigenspace is…

Q: Q.3: Express the matrix as a product of elementary matrices 2 0] [1 1 3 A = |0

A: Explanation of the solution is given below...

Q: 6. Give an example of two matrices, A and B, neither of which contains any zero entries whose…

A: Below mentioned a example related to this, you can construct many.

Q: 4. Verify whether the two given matrices are similar. Justify your answers Question a. [:] 1 1 3 1 A…

A: …

Q: [ 2 Find the inverse of the invertible matrix A = 5 -2

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Q: 2, 1 0 2 0 0 0 2 0 0 0 2 Are the matrices 2 1 and similar? Yes No 0 2

A: Given matrices are  210021002 and 200020002

Q: 2 3 Consider the matrix A = 1 1 2 |. Find the inverse of A, if -1 1 possible.

A:

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 ?

A:

Q: a. Prove that (A'B*)-1= (A-B-1)* and B are 3 x 3 matrices and %3D b. If |A| = 4 |B|= -1 compute…

A: I have used the property of  transpose and inverse of product of two matrices and then show the…

Q: 5. Find three 2 x 2 nonzero matrices A, B and C such that B C and AB = AC = 0.

A: To find the matrices A, B and C satisfying the given conditions.

Q: [2 0 01 Let A = 1 2 1 lo 1 21 Find two matrices that are similar to matrix A.

A:

Q: Example:1 Verify Cayley-Hamilton theorem for the matrix A= .2 41 and find its inverse. 3.

A:

Q: 7. Let A = (; ) (a) Express A- as a product of elementary matrices. (b) Express A as a product of…

A:

Q: 3. a. Give an example of two 2 × 2 matrices such that (A+ B)(A – B) # A² – B² b. State a valid…

A: