#### notes

For example , `3 xx [(2,4),(-5,1)]`

To get the result of matrix each element of the matrix multiply by 3.

The order of the above matrix is same as the order of the original matrix. The original matrix is of the order `2 xx 2` so the resulting matrix

will also be of the same order.

`3 xx [(2,4),(-5,1)] = [(3 xx 2,3 xx 4),(3 xx-5 ,3 xx 1)]`

=`[(6 , 12),(-15 , 3)]`

Thus `k xx [(a,b),(c,d)]` = `[(ka , kb),(kc , kd)]`

Multiplying a matrix to a number is called scalar Multiplication.

**Negative of matrix :**

Z = `[(1,3),(-5,2)]` -Z = ?

-Z = `-1 xx Z

=`-1 xx [(1,3),(-5,2)]`

=` [(1*-1 , 3*-1),(-5*-1, 2*-1)]`

=`[(-1 ,-3),(5, -2)] `

The negative of a matrix is denoted by –Z. We define –Z = (–1) Z.

**Difference of matrices:**

If A = `[a_(ij)]`, B = `[b_(ij)]` are two matrices of the same order, say m × n, then difference A – B is defined as a matrix D = `[d_(ij)]`, where `d_(ij) = a_(ij) – b_(ij)`, for all value of i and j. In other words, D = A – B = A + (–1) B, that is sum of the matrix A and the matrix – B.

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