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

Q: 3 2 0 3 4 0 0 0 2 Let A = Find ALL fixed points of the matrix A-".

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Q: 1 2 3 2 2 3 5 1 134 5 (b) Find the rank of the matrix A =

A: 1. We know rank of any matrix and rank of its reduced row echelon matrix are same. 2. Rank of 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: [1 0 -1] Find a matrix P which transform the matrix A= 1 2 1 to diagonal | 2 2 3 form. Hence A“.

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Q: 2 1 -1 3 1 2 1 2 0 b) Calculate the rank of the matrix P = 3 1 1 1 |-1 -5 -3 -7 3

A: Given,

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: |3 1 2 - Transpose of the Matrix 2 -1 2 |-1 2 3 1 2 -1 -2 2 -1 a. C. -2 -1 3 -2 3. 2. 1 -1 -1 -2 0…

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Q: 0 5 Let A= 4. diagonalizable matrix( A-XDX), then X and D are: 1 Select one: a. -5 X= -5 0 4 0. b.…

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Q: 1 0 2 A = |1 1 2 0 0 0 is Determine if the matrix diagonalizable. Justify your answer.

A: Given matrix is, A=102112000

Q: c. Find an orthogonal diagonalization of the symmetric matrix 1 -2 0 A = -2 1 4

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Q: 0 1 2 3 0 0 1 2 A = 0 0 0 1 12 - 0 0 0 0 A=[a] matrix can be expressed as

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Q: [A] Find all the minors and cofactors of the matrix 0. 2 1 A =| 3 -1 2 0 1] 4

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Q: 2 1 -1 3 1 9. Calculate the rank of the matrix P = | 2 1 2 0 3 1 1 1 |-1 -5 -3 -7 3|

A: P=210-131212003111-1-5-3-73

Q: 3 0 0 0 1 1 is an elemanter matrix. |\ 0 1 Choose one: true false

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Q: -1 2 4 Find the 1-norm of the matrix 3 -2 0 1 -1 2.

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Q: 3. Find a 3 x 3 matrix A such that [1 0 3] 1 1 0 0 1 0 2 1 11 A = 4 2 3 1 1

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

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Q: 2 1 0 -1 3 1 Calculate the rank of the matrix P = 1 2 0 3 1 1 1 -1 - 5 -7 3 -

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Q: 2 3. Let A be an invertible matrix such that A-¹ = 0 1 2 1 3 0 1 01 Solve the system (2A²)x= b,…

A: In this question we have to solve the system of equation.

Q: 1 -2 0 4 3 Calculate the rank of the matrix P = 1 1 -1 -5 -1 3 8 2 -12

A: The matrix P is,P=1-2043110-1-5-18382-12To find its rank.

Q: [1 0 2] 1 2 is diagonalizable. Justify your answer. 0 0 0 9. Determine if the matrix A = 1

A: If minimal polynomial having a repeated roots then that matrix is not diagonalzible.

Q: 0 5 Let A= diagonalizable matrix( A=XDX), then X and D are: 1 Select one: a. [5 O b. -5 X3D 5 0 O c.…

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Q: [2 3 4 3 4 5 6 20. Calculate the rank of the matrix P = 4 5 6. 7 9 10 11 12 'n

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Q: -2 -1 -3 1 Determine the rank of the matrix 1 0 1 -1

A: Rank of the matrix

Q: [2 0° 0 3 2. similar to matrix 1 ? 0 3 Is matrix

A: The matrices A and B are similar if there exists an invertible matrix P such that B=P-1AP

Q: [0 5 Let A= 4 1 diagonalizable matrix( A=XDX), then Xand D are: Select one: a. -5 -5 4 b. -5 =X 4…

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: 1 -1 2 a) Find the matrix A if (3A) =0 2 0 3 -1 4

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Q: 1 3 1 -1 0 1 Consider the matrix A = -3 2 1 -2 1 4 1 6 1 3

A: Let us apply elementary row operations on the augmented Matrix [A|b] to reduce it in row reduced…

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 4 0 3 2 1 -1 3 о 1 -1 0 0 0 5 0 0 0 0 4 der the matrix A = 1 3 8. 1.

A: In this question, the following conditions are checked. Lower triangular matrix. Diagonalizable.…

Q: 1 0.1 0.9 3 -12 6 Given Matrix A = 4. 1 -5 5 1. 17 6 -2

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Q: 0 5 Let A = diagonalizable matrix( A = XDX-1 4 1 ), then X and D are: Select one: а. 1 -5 X: 4 0 -4…

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Q: 2 0 0 3 -2 0 1 -1 Consider matrix A = -7 2 4 -2 0 0 5 Calculate det (A³) 1.

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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: 1 2 The adjoint of the matrix A =|-3 1 2 0 %3D -2 is

A: Given : Matrix A = 120-31-2201   To find : Adjoint of the given matrix?

Q: 1 2 4 Suppose matrix A: A=3 16 x 3 2 Determine the value of x if matrix A is singular.

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Q: 0 5 Let A =| diagonalizable matrix( A = XDX¯1), then X and D are: Select one: а. -5 X = 4 -5 4 b. 1…

A: Given A=0541

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: (1 2 3 2 (b) Find the rank of the matrix A = 2 3 5 1 1 3 4 5

A: The given matrix,A=123223511345

Q: [i -1 2 Find the matrix A if (5A)" =|0 2 0 2 0 |3 -1 4 %3D

A: If A is an invertible matrix then,

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

A: By  using the property  (AB)-1 = B-1A-1

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: 1 3 -4 -3 Find the nullspace of the matrix A = 0 1 0 0 -3 1

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Q: snip

A: The given equation is in the form: AX=B         -1 where,  A=10-123-1011 and B=-1-3503-2 It is to…

Q: 口 A 4) Identify the dimension of the transpose matrix. [1 0-1] [1 3 5 7] Y =0 3 1 1 8 9 58 -1 5 9 0…

A: Given a matrix and its transpose.

Q: [1 2 3] 4 5 6 7. 7 8 9 14. Find a symmetric matrix Q such that q(7) = T" Qu = "

A:

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: 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: 0 5 ] Let A diagonalizable matrix( [ 41 A=XDX, then X and D are: Select one: a. -5 1 -5 0 D= 4. 4.

A: Given  matrix A=0541we have to find  matrix X and D such  that A= XDX-1

Q: 1 0 3 2 1 1 4 4 0 3 3 6 Compute the reduced row echelon form of the matrix

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.