Mathematics
Introduction to matrices
आव्यूहों का परिचय
In this Class 12 Mathematics topic from the Matrix chapter, students are introduced to matrices as rectangular arrangements of numbers or expressions used to organise and represent information. They learn how to identify rows, columns, elements, and the order of a matrix, read standard notation, and distinguish common types such as row, column, square, zero, diagonal, and identity matrices. The topic builds the foundation for understanding matrix equality and later matrix operations.
Practice questions
If a matrix has (3) rows and (4) columns, how many elements does it have?In the matrix \(A=[a_{ij}]_{2\times3}\), what does \(i\) represent?What does (a_{23}) mean in the matrix (A=[a_{ij}])?What type of matrix is (A=\begin{bmatrix}1&0\\0&1\end{bmatrix})?Which matrix is a square matrix?What type of matrix is (A=\begin{bmatrix}5&0\0&5\end{bmatrix})?What is the value of \(a_{12}\) in \(A=\begin{bmatrix}1&2\\3&4\end{bmatrix}\)?What is the value of \(a_{21}\) in the matrix \(A=\begin{bmatrix}6&7&8\\9&10&11\end{bmatrix}\)?When are two matrices (A) and (B) called equal?If \(A=[a_{ij}]_{2\times2}\) and \(a_{ij}=i+j\), what is the value of \(a_{22}\)?If \(A=[a_{ij}]\) is a \(3\times2\) matrix and \(a_{ij}=2i-j\), what is the value of \(a_{31}\)?If (A=[a_{ij}]*{2\times3}) and (a*{ij}=i), what will the matrix (A) be?If \(A=[a_{ij}]\) is a \(2\times2\) matrix and \(a_{ij}=j\), what is \(A\)?In which type of matrix must the elements outside the main diagonal be (0)?What is the transpose (A^T) of (A=\begin{bmatrix}1&2\3&4\end{bmatrix})?If the order of (A) is (2\times3), what will be the order of (A^T)?In the matrix \(A=\begin{bmatrix}1&0\\0&2\end{bmatrix}\), what are the elements on the main (principal) diagonal?For the matrix \(A=\begin{bmatrix}0&5\\7&0\\end{bmatrix}\), which are the off-diagonal elements?Which statement gives the correct definition of a matrix?If (A=[a_{ij}]*{3\times3}), then (a*{13}) is the element at which position?