Square Matrix: Overview, Questions, Preparation

Matrices and Determinants 2021 ( Matrices and Determinants )

Rachit Kumar Saxena

Rachit Kumar SaxenaManager-Editorial

Updated on Jul 25, 2021 07:13 IST

What is Square Matrix?

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.

Weightage of Square Matrix in Class 12

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

Illustrated Examples on Square Matrix

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.

FAQs on Scalar Matrix

Q: What is an example of a diagonal matrix?

A: A square matrix, if and only if it is triangular and regular, is diagonal. Also, a symmetric matrix is any square diagonal matrix. As a matrix that is both upper and lower triangular, the asymmetric diagonal matrix can be identified. The identity matrix In is diagonal for every square zero matrix.

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

A: R * C represents the dimension of a matrix, where R is the number of rows in the matrix and C is the number of columns. If there are the same number of rows as columns in a matrix, it's a square matrix. Matrices with only one row are called row matrices, and column matrices are those with just one column.  

Q: Is a square matrix symmetric at all times?

A: Only square matrices can be symmetric since identical matrices have equal dimensions. As all off-diagonal elements are 0, any square diagonal matrix is symmetric. Therefore, it is also believed that a symmetric matrix corresponds to one that has real-valued entries in linear algebra over complex numbers.

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

A: A scalar is transposed by the same scalar. Along with (2), this states that the transpose is a linear map from the space of m × n matrices to the space of all n × m matrices. The determinant of a square matrix is the same as its transposing determinant.

Q: If there is a matrix equal to zero?

A: If a matrix determinant is negative, its rows are linear vectors, and its columns are linear vectors. A matrix's determinant is the oriented volume of the unit cube's graphic. If it is empty, the cube of the unit is mapped within a plane and has zero volume.

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