## Matrix MultiplicationIn mathematics, While we do addition or subtraction of matrices, we add or subtract the elements matching with the positions. But in matrix multiplication, we do not so. Instead of it, we perform the
## Note: While dealing with the matrix multiplication, remember that the number of columns in the first matrix must be equals to the number of rows in the second matrix. If the condition is not satisfied, the matrix multiplication is not possible.In matrix multiplication, it is not necessary that both matrices must be a square matrix, as in addition and subtraction. Suppose we have a matrix A of Let's understand it through an example. Suppose we have two matrices A and B of dimensions 2×3 and 3×2, respectively. The resultant matrix will be a 2×2 matrix. To find the (a,b,c).(p,q,r)=a×p+b×q+c×r To find the (a,b,c).(x,y,z)=a×x+b×y+c×z To find the (d,e,f).(p,q,r)=d×p+e×q+f×r To find the (d,e,f).(x,y,z)=d×x+e×y+f×z The resultant matrix is: ## Multiplication of a 2×2 matrix and 2×1 matrix## Multiplication of the two 2×2 matrix## Multiplication of 3×3 matrixSimilarly, we can find the multiplication of the matrices with different dimensions.
**Non-commutative:**AB ≠ BA**Associative:**A(BC) = (AB)C**Left Distributive:**A(B + C) = AB + AC**Right Distributive:**(A + B)C = AC + BC**Scalar:**k(AB)=(kA)B (where k is scalar)**Identity:**IA=AI=A**Transpose:**(AB)^{T}=A^{T}B^{T}
The dimensions of the matrix A and B are 1×4 and 4×1, respectively, so the resultant matrix will be of dimension 1×1. A×B=[2×7+5×2+6×3+8×9] A×B=[114]
The dimensions of the matrix A and B are 3×2 and 2×1, respectively, so the resultant matrix will be of dimension 3×1.
We know that the identity matrix is the matrix whose principal diagonal elements are 1 and other elements are zero is called an
We have to find A×(-A) or -A The negative matrix of the matrix A is -A. It means to multiply each element of matrix A by the negative sign. Next TopicEquivalent Fractions |