How many free variables does each augmented matrix have?

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

A:

Q: Define Square matrix?

A: A matrix is the arrangement of data in rows and columns.

Q: Write down the 4×4 3D matrix to scale an object by 50% in all directions.

A: We have to write down the 4×4 3D matrix to scale an object by 50% in all directions.We know…

Q: Show that a square matrix which has a row or a column consisting entirely of zeros must be singular.

A: Consider a square matrix A=000123456 and B=140250360 Here, all the elements of first row of the…

Q: Provide an example of an elementary matrix for each of the three types of row operations and clearly…

A: The three types of elementary row operations on a matrix : (1) Interchange two rows (2) Multiply…

Q: Construct the augmented matrix

A: We first write the given equations in standard form

Q: What is the multiplicative identity matrix?

A: According to the question, we have to define the multiplicative identity matrix. As the above…

Q: If the nulI snace of a 30x17 matrix is 13-dimensional, find the rank of the matrix.

A: We have been given the matrix which is of 30 x 17 i.e it has 30 rows and 17 columns. And it is also…

Q: Show that every diagonalizable matrix has a square root.

A: Square Root Matrix of a Diagonalizable Matrix is Diagonalizable. A is diagonalizable. Therefore,…

Q: When two m x n matrices are said to be equal? Explain there Applicability?

A: Two mxn matrices are said to be equal if their corresponding elements are equal.

Q: Can the null space of a 3 × 6 matrix have dimension 2? Explain.

A:

Q: Show that for a square matrix A, AAT is a symmetric matrix.

A:

Q: Determine whether the following matrix is invertible by finding its determinant. 4 -14 -56

A: Consider the matrix 14-14-56