Let A be an m xn matrix. Explain why the matrix ATA is symmetric.

Q: Can you provide one image or figure of the hermitian matrix?

A:

Q: Show that the matrix is not diagonalizable.

A:

Q: Determine if the matrix, M is diagonalizable. Show your complete solution. 25

A:

Q: Suppose A is an m x n matrix whose columns are linearly independent. What is the nullity of A?

A: Given A is an m×n matrix whose columns are linearly independent. We have to find the nullity of A.

Q: Determine whether the matrix is symmetric, skew-symmetric, or neither. A square matrix is…

A: Given matrix is

Q: what is a Hermitian matrix? does every Hermitian matrix has to be square matrices?

A:

Q: Explain why the matrix A + C does not exist.

A:

Q: Let the matrix below be Anti-symr

A: Anti symmetric matrix is also known as skew symmetric matrix.

Q: If the matrix A is positive symmetric definite, is BTAB also positive symmetric definite?

A: Let us define the function as, A¯=BTAB Then, A¯T=BTABT=BATBT=BABT   [A is symmetric]

Q: 32. Construct a nondiagonal 2 x 2 matrix that is diagonalizable but not invertible.

A: .

Q: Give an example of a matrix M where MMT and MTM are not equal matrices.

A:

Q: Let A be square matrix. If A" = 0. A= Oava %3D for n> 2. Then

A:

Q: Is it possible for A3 to be an identity matrix without A beinginvertible? Explain.

A: To explain:It is possible for A3 to be an identity matrix without A being invertible.By definition

Q: Give an example of a 3 x 3 lower triangular matrix A that is not diagonal. A =

A: We write the 3x3 lower triangular matrix which is not diagonal

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

A:

Q: Give an example of a 2 x 2 matrix A such that im(A) =ker(A). %3D

A: Null space of a linear transformation: T:V(F)→V'(F) be a linear transformation then the null space…

Q: If A is a real n xn matrix, show that AA" and ATA are similar. (Hint. Start with an SVD for A.)

A:

Q: Find three non-trivial 2 x 2 matrices such that the square of the matrix is the zero matrix, i.e: A?

A: We want to find matrix A such that A2 = 0000

Q: Let A be a 4x6 matrix. what is the dimension of Col A if the nullity is 2? Explain

A: 4

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 diagonal matrix D is similar with A a A =[? -5 And make sure can transtor diagomalizablewith

A:

Q: Let A be an n × n matrix and let B = A + I. Is it possible for A and B to be similar? Explain.

A:

Q: Find a 2 x 2 matrix such that -3 1

A:

Q: Let A be a 3x6 matrix of rank 3 then nullity of A equal 0 Select one: O True O False

A: From rank plus nulity theorem we know that : rank A + nullity A = the number of columns of A  From…

Q: Let A be an n × n singular matrix. Then

A: if matrix A is singular that means its determined is zero.so at least one row of matrix A is…

Q: Give an example of a 3 x 3 upper triangular matrix A that is not diagonal. A =

A:

Q: An n x n matrix that is orthogonally diagonalizable must be symmetric.

A:

Q: the matrix A = and explain why or why not this matrix is diagonalizable

A: In the given question, concept of diagonalizable matrix is applied. Diagonalizable Matrix Any square…

Q: Let A be an m x n matrix. Is ATA symmetric? Explain.

A: Given that, A is an m×n matrix

Q: What does it mean to say that A is a matrix with dimensionm  n?

A: A matrix is a rectangular array of elements arranged in rows and columns. The size of the matrix is…

Q: A matrix that is both upper and lower. triangular is called diagonal ylgn ihi

A: Upper and lower triagular matrix

Q: Explain why the columns of an n×n matrix A span R^n when A is invertible.

A: Consider, a matrix A of order n, which is a invertible matrix.Since, the set of vectors

Q: a) Let A be a 3 x 5 matrix

A: For the multiplication of two matrix the number of columns in first matrix is equal to the number of…

Q: Show that the matrix B′AB is symmetric or skew symmetric according as A is symmetric or skew…

A: Show that the matrix B′AB is symmetric or skew symmetric according as A is symmetric or skew…

Q: Let A be an m × n matrix. Explain why the matrix multiplications ATA and AAT are possible.

A:

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: What is the condition for a diagonal matrix to be orthogonal?

A: use the properties of orhtogonal with respect to a diagonal matrix...

Q: Explain transpose AT of the m x n matrix A?

A:

Q: For a square matrix A, AAT = ATA. %3D A) True False

A: We have to find the given statement is true or false.

Q: Find the trace of the matrix A =

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: Consider a matrix A, and let B= rref(A). %3D a. Is ker(A) necessarily equal to ker(B)? Explain. b.…

A: The matrix B=rrefA is the Reduced Roe Echelon form of the matrix A. The kernel of a matrix A is the…

Q: Determine whether the matrix B = is awesome or not. %3D

A: 7.1 To determine whether the matrix B is awesome or not. Where  B=i2−3232−i2and B is awesome if…

Q: Give an example of a nonzero 3 x 3 diagonal matrix A. A =

A: Diagonal Matrix: In linear algebra, a diagonal matrix is a matrix in which the entries outside the…

Q: Let A be a matrix with more columns than rows.

A:

Q: A matrix which is not a square matrix is called a .6 Matrix

A: 6)  A matrix which is not a square matrix is called a

Q: Write down what it means for a n x k matrix to be singular.

A: As we know, If matrix is singular then it has determinant equals to '0' For Finding determinant…

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.