Approach:
Fundamental Matrix operations are equality, addition, subtraction, multiplication by a scalar and multiplication.
Equality: Two matrices [A] and [B] are said to be equal if and only if matrices are of same order and the corresponding entries are the same.
Addition: When two matrices A and B are added, the resulting matrix [C] is obtained if and only if the both matrices are of same order and the entries are found by adding the corresponding entries.
Subtraction: When matrix B is subtracted from [A], the resulting matrix [C] is obtained if and only if the both matrices are of same order and the entries are found by subtracting the entries of [B] from the corresponding entries of [A].
Multiplication by a scalar: If a matrix [A] is multiplied by the scalar (real number) x, the resulting matrix is the matrix in which each entry is multiplied by x.
Multiplication: Let [A] be an m×r matrix and [B] be an r×n matrix. The product of AB=[C] is an m×n matrix. The entry in the i th row and j th column of [A][B] is the sum of the products formed by multiplying each entry of the i th row of [A] by the corresponding entry in the j th column of B.
Check whether the number of columns of [A] is equal to the number of rows of [B]
Calculation:
Given matrix operation is CB-3D
B=2-10101 C= 2012-11 D=010-10001-1
In order to multiply two matrices, columns of first matrix should be equal to rows of the second matrix.
Check whether the number of columns of [C] is equal to the number of rows of [B].
C=3×2,B=2×3
Therefore, CB=3×3 matrix.
CB= 2012-112-10101
=2×2+0×12×-1+0×02×0+0×11×2+2×11×-1+2×01×0+2×1-1×2+1×1-1×-1+1×0-1×0+1×1
=4+0-2+00+02+2-1+00+2-2+11+00+1
=4-204-12-111
3D=3010-10001-1
=3×03×13×03×-13×03×03×03×13×-1
=030-30003-3
CB-3D=4-204-12-111-030-30003-3
=4-0-2-30-04--3-1-02-0-1-01-31--3
=4-507-12-1-24
Final statement:
The matrix operation of CB-3D=4-507-12-1-24