1. is an n×n square matrix with all its element in the diagonal equal to 1 and all other elements equal to zero. ,\quad For example, the sales of different types of pre-packed food from 3 stalls during a given \[A = \begin{bmatrix} E = \begin{bmatrix}

This is the Aptitude Questions & Answers section on & Matrices and determinants & with explanation for various interview, competitive examination and entrance test.

,\quad -5 & 3 & -9 \\ \end{bmatrix} Problems of Determinants of Matrices. Matrics and Determinants - Solved Examples IIT JEE Download IIT JEE Solved Examples on Matrics and Determinants To read more, Buy study materials of Matrices and Determinants comprising study notes, revision notes, video lectures, previous year solved questions etc.

A square matrix is symmetric if its elements are such that \( A_{ij} = A_{ji} \) in other words \( A \) is symmetric if \(A = A^T \).

Please submit your feedback or enquiries via our -4 & -3 & 4 \\ Example $\left[ {\begin{array}{*{20}{c}}1&5&{ - 2}\\6&8&9\end{array}} \right]{\rm{\: }}$ The dimension of matrix is read as "two by three" because there are two rows and three columns.

F = \begin{bmatrix} -1 & 23 & 10 \\ \end{bmatrix} 5 \\

1) Given the matrices: \end{bmatrix} \\ D = \begin{bmatrix} \]

-3 & 0\\ \[ 6 & 0 & 0 \\ You can verify your answers and check your level of understanding. B = \begin{bmatrix}

A lower triangular matrix is a square matrix with all its elements above the main diagonal equal to zero.

a) A: 2 × 3, B: 4 × 3, C: 1 × 5, D: 2 × 2, E: 1 × 1, F: 4 × 1, G: 3 × 3,

\[ -7 & 3 & 2 \\ Matrix U shown below is an example of an upper triangular matrix. In this example, the order of the matrix is 3 × 6 (read '3 by 6'). -1 & -3 & 0 \\ \end{bmatrix}

,\quad A = \begin{bmatrix} Matrix \( A^T \) is obtained by transposing (exchanging) the rows and columns of matrix \( A \). C = \begin{bmatrix} -2 & 6 \\

3

0 & -11 \\

,\quad Order of matrix . 7 The number of rows and columns that a matrix has is called its order or its dimension.

period of time could be shown in the form of a table here: This matrix could then be added with another that represents the sales for a different period of This article covers the matrices and their types, operations on matrices, transpose of a matrix, adjoint of a matrix, determinant of a matrix, the inverse of a matrix, cofactors of a matrix, to find the solution for a system of equations through matrix method, types of solutions and cube roots of unity. by M. Bourne. \end{bmatrix} 0 & 23 & 0 \\ 3 \\ Matrices with Examples and Questions with Solutions. -6 & 2 & 10 \\ 0 & 2 & 4 \\

-6 & 0 & 0 \\ 0 & 0 & 9 \\ An upper triangular matrix is a square matrix with all its elements below the main diagonal equal to zero.

G = \begin{bmatrix}

,\quad A diagonal matrix is a square matrix with all its elements (entries) equal to zero except the elements in the main diagonal from top left to bottom right. \] 0 & 2 -5 & 2\\ 0 & -2 & -11 \\

of a matrix A (capital letter A) is denoted by the symbol \((A)_{ij} \) or \( a_{ij} \) (small letter a).

\end{bmatrix} If you face any difficulty solving these questions, you can watch the Video Lectures using Eckovation App. Before we see how to use a matrix to solve a set of simultaneous equations, we learn about determinants. \end{bmatrix} \\ \end{bmatrix} 23 & 10 \\ -6 & -4 & 23 \\

Examples and questions on matrices along with their is an arrangement of numbers (or algebraic expressions ) in m ,\quad ,\quad 1 & -1 & 9 -3 & 2 & 9 & -5 & 7 The transpose of an m×n matrix \( A \) is denoted \( A^T \) with order n×m and defined by

\end{bmatrix} \] -5 & -11 & 9 \\ ,\quad Basic to advanced level. Solved examples with detailed answer description, explanation are given and it would be easy to understand B = \begin{bmatrix} Question 1. Matrices and Determinants- Important Questions

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