Given that matrices A and B are of order 3 x n and m x 5 respectively, then the order of matrix C = 5A + 3B is:
Determinants are mathematical expressions that can be computed from a square matrix. They are used in various applications including solving systems of linear equations and finding areas or volumes. For a matrix, the determinant provides important properties such as invertibility. If the determinant is zero the matrix is singular. Key operations include cofactor expansion and calculating determinants for 2×2 and 3×3 matrices.
Class 12 Maths Chapter 3 on Determinants involves square arrays of numbers used to solve systems of linear equations. Topics include properties of determinants calculation of 2×2 and 3×3 determinants cofactor expansion adjoint method Cramer’s rule and applications like finding areas of triangles and solving linear equations. Determinants are important in algebra and geometry for various mathematical problems.
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Matrix A has order 3 × n, and B has order m × 5; find the order of matrix C = 5A + 3B
Step 1: Rules governing addition of matrices
Addition is defined only when both matrices are the same order, and the same with our scenario of A versus B.
Matrix A has order 3 × n and matrix B has order m × 5.
For the addition 5A + 3B to be possible, we must have n = m, meaning both matrices must have the same number of columns.
Step 2: Order of matrix C
Once the condition n = m is met, then the matrix C that results from it will be of the same order as that of A and B, which is 3 × 5.
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