Square Matrix: Overview, Questions, Preparation

It is said that a n*n matrix is a square matrix of order n. In other words, a matrix is considered a square matrix if the number of rows and the number of columns in the matrix are equal.

Determinant of matrix

A scalar value computed for a given square matrix is the determinant of a matrix. The determinant is dealt with by linear algebra, calculated using the components of a square matrix. It can be assumed to be the scaling factor for a matrix transformation. Useful in solving a linear equation method, calculating the reciprocal of operations in a matrix and calculus. The determinant is seen geometrically as the volume scaling factor of the matrix-defined linear transformation. It is also represented as the n-dimensional parallelepiped volume crossed by the matrix's column or row vectors. As per linear mapping, the determinant is positive or negative, retaining or changing the n-space orientation.

In Class 12, you will get to learn it in the chapter Matrices and the weightage is 7-8 marks.

1. Is 1x1 a matrix of squares?
Solution.

A matrix of 1x1 is a scalar. For all of its entries, a null matrix has 0. If the number of rows in a matrix is equal to the number of its columns, the matrix is square. A matrix's main diagonal consists of the elements whose indices of rows and columns are the same.

2. What is a 3x3 matrix adjunct?
Solution.

The transpose of the cofactor matrix of A is the assistant of a matrix A. It is marked by ADJ A. An adjoint matrix is often referred to as a matrix adjugate.

3. A given matrix has 24 elements. Determine the possible order.

Solution.

A matrix has mn elements if it is the order m x n. The ordered pair is (6,4) (4,6) (8,3) (3,8) (12,2) (2,12) (24,1) (1,24). The order is 6x4 4x6 8x3 3x8 12x2 2x12 24x1 1x24.

Q: What is an example of a diagonal matrix?

Q: How can you find the matrix of a square?

Q: Is a square matrix symmetric at all times?

Q: What is the transposition of a matrix of squares?

Q: If there is a matrix equal to zero?