If order of matrix A is 2 x 3 of matrix B is 3 x 2, and of matrix C is 3 x 3, then which one of the following is not defined?
A matrix is a rectangular array of numbers arranged in rows and columns. It is used to represent data or solve mathematical problems. Matrices are involved in various operations like addition multiplication and inversion. They are fundamental in linear algebra and applied in physics engineering and computer science.
Class 12 Maths Chapter 3 covers Determinants which are square arrays of numbers used in solving systems of linear equations. Topics include properties of determinants determinant of 2×2 and 3×3 matrices cofactor expansion adjoint method Cramer’s rule and applications in finding areas of triangles and solving linear equations. Determinants play a key role in algebra and geometry.
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– Matrix A has order 2 × 3 and matrix B has order 3 × 2.
– The transpose of matrix B, B’, has order 2 × 3.
– For the sum A + B’, both matrices have order 2 × 3, so the addition is possible.
– However, matrix C has order 3 × 3, and for matrix multiplication to be defined, the number of columns in matrix C (3) must match the number of rows in A + B’ (2).
– Since 3 ≠ 2, multiplying matrix C by A + B’ is not defined.
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