A matrix of order m x 1 is called a Choose.

Q: Give an example of a 3 x 3 skew-symmetric matrix A that is not diagonal. A =

A:

Q: 1.) Let A = Obtain a matrix that is similar to A.

A:

Q: Let A be an m×n matrix with rank m and B be an n×p matrix with rank n. Determine the rank of AB.…

A: This can be done as follows:

Q: 2. Suppose A is a square matrix. Which matrix is not symmetric? O A+AT O AAT ОА-АТ O ATA

A: Note the following results if A and B are two matrices ABT=BTAT…

Q: A matrix A is said to be skew symmetric if AT = −A. Show that if a matrix is skew symmetric, then…

A:

Q: If S = A + iB is a Hermitian matrix, are its real and imaginary parts symmetric?

A:

Q: An n x n matrix A is invertible if and only if it is row equivalent to I. 'n' O True O False

A:

Q: If A is an m x n matrix then A' A and A have the same rank. true false

A:

Q: If A can be row reduced to the identity matrix, then A is not invertible. True False

A:

Q: Consider an n x n matrix. Give 3 equivalent conditions for A to be invertible

A: Let A be an n×n matrix. we have to give 3 equivalent condition for A to be invertible. Conditions…

Q: (b). Find out the similar matrix of given matrix:

A: Similar Matrices: Ant two matrices A and B are said to be similar if there exists an invertible…

Q: .

A:

Q: If A=XDX−1 where  X is a diagonalizing matrix of A, then 7X is also a diagonalizing matrix of A.…

A: Given: Where, X is a diagonal matrix of A, then 7X is also diagonalizing matrix of A. To determine:…

Q: Show that any nX n matrix can be written as the sum of a symmetric matrix and a skew-symmetric…

A: To show that any n x n matrix can be written as the sum of a symmetric matrix and a skew-symmetric…

Q: Find the range of a (2 × 3) matrix B with rank(B) = 2

A:

Q: A matrix A is similar to matrix B, if for some invertible matrix P, B = P''AP. Is B similar to A?

A:

Q: If A is a skew-symmetric matrix of order 5 then adj(adj(A5«5)) = %3D

A:

Q: the null space, and the row space of the matrix A.

A:

Q: Consider the multiplication AB is existing with the size (M × N) , where B is a matrix of size (L ×…

A: Consider the given information. The multiplication of two matrix is possible if and only if the…

Q: If A is a symmetric matrix, then At = |A| A diagonal matrix

A:

Q: If A is a square matrix such that some row of A2 is a linear combination of the other rows of A2,…

A:

Q: Let A be the matrix a- [}] 3 1 A = Which answer is correct for the A ?

A: GivenA=3121

Q: If A is a square matrix such that A =1, then A'is equal

A: Given, A is a square matrix such that A2=I.

Q: If A is a 6 × 8 matrix, what is the smallest possible dimension of Nul A?

A: Consider the provided matrix, Given, A is a 6 x 8 matrix. Since, the rank of A equals the number of…

Q: A matrix A is similar to matrix B, if for some invertible matrix P, B = P''AP. Prove that if A is…

A:

Q: (1.) Let A = Obtain a matrix that is similar to A.

A:

Q: 4. A matrix A is similar to matrix B, if for some invertible matrix P, B = P'AP. Is B similar to A?

A:

Q: Show that if A is an upper triangular matrix, then AT is lower triangular.

A: Given, A is an upper triangular matrix

Q: Which of the following is a lower triangular matrix?

A: GIVEN - MATRICES ARE GIVEN TO FIND - LOWER TRIANGULAR MATRIX  CONCEPT - IN LOWER TRIANGULAR MATRIX…

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

A:

Q: Enter a 3 x 3 skew-symmetric matrix A that has entries a12 = 1, a13 = 3, and a32 = 4.

A: Skew Symmetric Matrix: If the transpose of a matrix A is equal to the negative of itself then the…

Q: 2. Let A be a 7 x 5 matrix, and suppose AB is a 7 x 9 matrix for some matrix B. What must the size…

A: We know that matrix multiplication is possible only when number of column of first matrix is equal…

Q: An n x n matrix A is invertible if and only if it is row equivalent to I. O True False

A: Given statement is "An n×n matrix A is invertible if and only if it is row equivalent to In."

Q: If an nxn matrix A is invertible, then the rowa of A' are linearly independent. T O True O False

A: If a matrix is invertible then its rows are linearly independent

Q: Find a matrix P that will diagonalize A. Then use it to find A13 in a computationally efficient way.…

A:

Q: 2. Choose the rank of the matrix AT

A:

Q: Give an example of a 4 by 4 matrix A, which is not symmetric, however A is symmetric.

A: A square matrix is said to be symmetric if it is symmetric about the main diagonal.

Q: If A is a skew-symmetric matrix of order 5 then adj(adj(A5x5)) =

A:

Q: Consider an n x p matrix A and a p x m matrix B. If ker(A)-im(B), what can you say about the produet…

A:

Q: Find x such that the matrix is singular.

A:

Q: Suppose A is a matrix of order p × q and B is a matrix of order q × r, then illustrate the order of…

A:

Q: If A is a 2 x 2 skew symmetric matrix, must det(A) = 0?

A: we have a 2×2 skew symmetric matrix.

Q: If Ā is a 5 × 5 skew symmetric matrix, show that det Ā = 0.

A: A n×n order matrix A= is said to be skew symmetric matrix if the following condition hold…

Q: ) If A is a square matrix such that some row of A² is a linear combination of the other rows of A²,…

A:

Q: If A is a skew-symmetric matrix, then for all /, we have a, = 0. Select one: O True False

A: Given: a skew-symmetric matrix A To find: we need to check weather ajj=0, true or false for all j

Q: If A is an invertible matrix and det(A) = 7, what is det (A-1)?

A: Given: If A is an invertible matrix and det(A) = 7 To find: what is det (A-1 )?

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.