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Matrices And Determinants

Matrices and Determinants is an important topic in algebra that deals with arranging numbers in rows and columns and using them to solve mathematical problems. These concepts are widely used in mathematics, engineering, computer science, and economics. A matrix is a rectangular array of numbers arranged in rows and columns. Matrices are used to represent and solve systems of linear equations and perform various mathematical operations. A determinant is a special value calculated from a square matrix. Determinants are mainly used to find the inverse of a matrix and to solve systems of linear equations.

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Quick Revision of Matrices And Determinants
This PDF contains brief and easy-to-understand notes for the Matrices and Determinants chapter (MHT-CET Maths). All the important concepts, formulas, and properties are explained in a short and clear format for quick revision. Topics covered in this PDF: • Definition and order of matrices • Types of matrices (row, column, square, identity, diagonal) • Matrix operations (addition, multiplication, scalar multiplication) • Transpose of matrix • Determinants and their calculation • Minors and cofactors • Adjoint of a matrix • Inverse of a matrix • Properties of determinants • Solving linear equations using matrices

Formula Bank

Scalar Multiplication
If\space k\space is\space ascalar\space𝑘𝐴=[𝑘𝑎𝑖𝑗]
Transpose of Matrix
(A^{T})ij=aji
Determinant (2×2)
\begin{pmatrix}a & b\\ c & d\end{pmatrix}=ad-bc
Cofactor
Cij=\left(-1\right)^{i+j}.Mij
Adjoint of Matrix
adj(A)=\space\space\left(cij\right)^{T}

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Assessment 1: MCQ1