Mathematics
Matrix
आव्यूह
In Class 12 Mathematics, the chapter Matrix introduces matrices as rectangular arrangements of numbers and develops their order, types, and equality. Students learn matrix addition, scalar multiplication, and multiplication, including the conditions that govern these operations. The chapter also explains transpose, symmetric and skew-symmetric matrices, and invertible matrices, helping students use matrix properties accurately in algebraic problems.
1Introduction 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.
25 questionsOrder of a matrix
आव्यूह का क्रम
In this Class 12 Mathematics topic from the Matrix chapter, students learn that the order of a matrix describes its size as the number of rows × number of columns, written m × n. They practise identifying rows and columns, writing the order of a given matrix, and recognising when two matrices have the same order. Examples help distinguish square, row, and column matrices, while reinforcing that order depends on arrangement—not on the values of the entries. This foundation supports later work with matrix operations and equality.
9 questionsTypes of matrices
आव्यूहों के प्रकार
In Class 12 Mathematics, this topic introduces the main types of matrices covered in the Matrix chapter. Students learn to identify and distinguish row, column, rectangular, square, zero, diagonal, scalar, identity, upper triangular, lower triangular, symmetric and skew-symmetric matrices by examining their order and entries. They also practise expressing matrices in standard forms, checking defining conditions, and understanding how these classifications support later work with matrix operations, determinants and linear equations.
11 questionsEquality of matrices
आव्यूहों की समानता
In this Class 12 Mathematics topic from the Matrix chapter, students learn when two matrices are considered equal. They examine the requirement that both matrices have the same order and that every pair of corresponding elements is equal. The topic also shows how matrix equality can be used to compare entries, form equations, and find unknown values. Clear examples help students apply these conditions accurately in algebraic problems.
3 questionsAddition of matrices
आव्यूहों का योग
In this Class 12 Mathematics topic from the chapter Matrix, students learn how to add two or more matrices by combining their corresponding elements. The topic explains the essential condition for matrix addition—that the matrices must have the same order—and develops accuracy in identifying rows, columns, and matching positions. Students practise finding sums, understanding properties such as commutativity and associativity, and applying matrix addition in structured mathematical problems.
0 questionsScalar multiplication
अदिश गुणन
In Class 12 Mathematics, scalar multiplication explains how a matrix is multiplied by a single number, called a scalar. Students learn to multiply every entry of the matrix by that number and understand the effects of positive, negative, fractional, and zero scalars. The topic also develops fluency with matrix properties and operations, including distributive and associative relationships, helping students simplify matrix expressions and apply them accurately in algebraic calculations.
0 questionsMultiplication of matrices
आव्यूहों का गुणन
In this Class 12 Mathematics topic from the chapter “Matrix,” students learn how to multiply two matrices using the row-by-column rule. They identify when multiplication is possible by comparing the dimensions of the matrices, calculate each resulting entry through the dot product of a row and a column, and determine the order of the product matrix. The topic also develops understanding of important properties, including associativity, distributivity, identity matrices, and why matrix multiplication is generally not commutative.
0 questionsTranspose of a matrix
आव्यूह का ट्रांसपोज़
In this Class 12 Mathematics topic from the chapter Matrix, students learn how to form the transpose of a matrix by interchanging its rows and columns. They practise writing the transpose using the notation Aᵀ, identify how the order changes from m × n to n × m, and verify key properties such as (Aᵀ)ᵀ = A and (A + B)ᵀ = Aᵀ + Bᵀ. The topic also builds understanding of symmetric matrices and prepares students for further matrix operations.
1 questionsSymmetric matrix
सममित आव्यूह
In Class 12 Mathematics, the topic Symmetric Matrix introduces a special type of square matrix studied in the Matrix chapter. Students learn to identify a matrix whose transpose is equal to the original matrix, written as A = Aᵀ, and understand how its entries mirror each other across the main diagonal. The topic also develops skills in checking examples, writing symmetric matrices, and applying their basic properties in matrix-based problems.
0 questionsSkew-symmetric matrix
विषम-सममित आव्यूह
In Class 12 Mathematics, under the chapter Matrix, students learn to identify and work with skew-symmetric matrices. A square matrix A is skew-symmetric when its transpose satisfies Aᵀ = −A, so each pair of corresponding off-diagonal entries has opposite signs and every diagonal entry is zero. The topic develops skills in testing this condition, forming examples, comparing matrix entries, and applying transpose and matrix-operation concepts to solve related problems.
0 questionsInvertible matrices
व्युत्क्रमणीय आव्यूह
In Class 12 Mathematics, this topic from the Matrix chapter introduces invertible matrices—square matrices that have a multiplicative inverse. Students learn the condition for invertibility, namely that the determinant is non-zero, and understand how the inverse relates to the identity matrix. They practise finding inverses using the adjoint method and elementary transformations, verify standard properties, and apply matrix inverses to solve systems of linear equations.
0 questions