4- Determine the rank of the following matrices: 2 8] [3 4 5 [1 7 6 ii- A=1 2 3 5 3] [3 9 21 iii- A = |1 5 6 l2 7 4 i- A = 4 [4 5 6

Q: Let A be an nxn matrix and B= A+ I, where / is the identity matrix, then it is possible for A and B…

A:

Q: Generally the matrices are denoted by Select one: a. capital letter b. small letter c. numbers d.…

A: Generally matrices are denoted using capital letter.

Q: For a matrix A: -101 0 0 0 10-1 Find the orthogonal complement of Im (TA)

A: Orthogonal complement of the space

Q: Let A, B be  matrices of the same order. Then det(A+B)=det(A) + det(B).  True or false

A:

Q: 1 2 A= -2 4 -2 4 3 5 -1 5 4 3 3 7 6 6

A:

Q: Use the partitioned matrix technique to find the inverse of: 1 0 0 3 1 4 -5 -1 -1

A: This question is based on Matrix.

Q: Find inverse of the following matrix-: b' а A =

A:

Q: O True

A: True

Q: Evaluate det (A) for the matrix A=($ 2).

A: Given matrix is A=8254 The task is to find the inverse of the given matrix.

Q: Characterize the image and kernel of the following matrices: 1 (443) -2 2 2

A:

Q: 2. Calculate the following matrix products: 1 -1 -1 3. A.

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Q: Let A and B be n x n invertible matrices. Use matrix algebra to simplify A(A¯¹ + B¯¹)B.

A:

Q: Compute eA for each of the following matrices:

A:

Q: Find the inverse of the matrix:                    3 3 4                    2 3 2…

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Q: ) Write the following matrix as a product of elementary matrices: H 1 1 0 02 -3 1

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Q: Let A and B be two 4 × 4 matrices with rank(A)<4. Then rank(A²B)<4. Select one: O True O False

A:

Q: Find the rank of the following matrices: 1 2 2 3 3 2 1 тank(A)— 2 3 таnk(A)—

A: We use the definition of the rank of a matrix to find the rank of given matrices.

Q: determine which of the following matrices are nonsingular:

A: to determine the matrix which is non singular.

Q: ices with the same size, then (AT + B")":

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Q: Determine the order of the following matrix: [[9,-5], [0,0]]

A: Order of the matrix is expressed as  Number of Rows X Number of Columns

Q: Define Similar Matrices.

A: Similar Matrices: Let A and B are two square matrices, then A is said to be similar to B if there…

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:

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.