mathematics multiplication & division more: cseindex mathematicsmultiplication&division

Let A be a matrix of order mxn. Let B be a matrix of order nxp. Then the product of the matrices A and B is of order mxp. i.e., when we multiply two matrices the number of columns of the first matrix should be equal to the number of rows of the second matrix. Two matrices can be multiplied by usin..

Matrix multiplication is not commutative in general. Matrix multiplication is associative i.e., (AB)C = A(BC), whenever both sides are defined. Matrix multiplication is distributive over matrix addition i.e., (i) A(B + C) = AB + BC (ii) (A + B)C = AB + AC wh..

The inverse of a square matrix if it exists, is unique. Let A be an invertible square matrix. If possible, let B and C be two inverse of A. Then AB = BA = I. AC = CA = I (by def. of inverse) Now, B = BI = B(AC) = (BA)C [ Matrix multiplication is associative] = IC = C i.e., B = C Hence t..

Equality of Matrices, Addition of Matrices, Matrix Addition is commutative, Matrix addition is associative, Subtraction of Matrices, Multiplication of a matrix by a scalar, Multiplication of Matrices, Properties of Matrix Multiplication, Transpose of a Matrix, Pr..

>If A, B and C are the matrices which can be multiplied then (a) Matrix multiplication is not commutative, i.e., AB BA (always) (b) Associative law holds good for matrix multiplication, i.e., (AB)C = A(BC) (c) Matrix multiplication is distributive with respect to addit..

If the rows and columns of a determinant are inter-changed, the value remains unaltered. If any two rows (columns) of a determinant are identical, its value of the determinant is zero. If any two rows (columns) of a determinant are interchanged, the value of the determinant is (-1) times th..

Find the multiplicative inverse of x + 2. => 1 x + 1 2 or x - 2 or 1 x + 2 or x + 1 2..

What is the LCM of two numbers ' a ' and ' b ', if b is a multiple of a ? => a or ab or b or a + b..

Multiplication of Matrices - Let us consider the sales done by a school canteen for two successive days. Monday 25 cokes 12 cakes Tuesday 40 cokes 7 cakes Each coke costs $ 5 and cake costs $ 10. The sales can be expressed as a 2 x 2 matrix and the price as a 2 x 1 matrix as given below: ..

Let us consider the sales done by a school canteen for two successive days. Monday 25 cokes 12 cakes Tuesday 40 cokes 7 cakes Each coke costs $ 5 and cake costs $ 10. The sales can be expressed as a 2 x 2 matrix and the price as a 2 x 1 matrix as given below: The amount collected for two days can b..