## Tuesday, May 6, 2008

### Matrices - 1

Matrices will be an easy topic, but speed is required in doing various arithmetic calculations and some calculations to solve equations to get the answers.

For example a problem is given in 2006 in comprehension where matrix A is given.

From AX1 = B1 you are asked to find X1, from AX2 = B2, and Ax3 = B3 you have to find X2 and X3. You are asked to make matrix [X1 X2 X3], then find its determinant, and then its inverse and then [R1][X][C1]

All questions are straight forward but computation is involed and you have to do fast.

Concepts

1. A matrix is a rectangular array of numbers [a0]
2. A matrix with m rows and n columns is called an m×n matrix and the size or dimension of this matrix is said to be m×n.
3. Tow matrices are said to be equal provided they are of the same dimension and corresponding elements of the two matrices are equal.
4. A matrix is termed as square matrix if m = n or its size is m×m.
5. A matrix is termed as row matrix if m = 1
6. A matrix is termed as column matrix if n = 1
7. A matrix is termed as null or zero matrix if a0] = 0 for all i and j.
8. A matrix is termed as diagonal matrix if a0] = 0 for all ij where i is not equal to j.
9. A matrix is termed as scalar matrix if a0] = 0 for all ij where i is not equal to j and a0] = constant (k) for all i and j.
10. A matrix is termed as identity matrix or unit matrix if a0] = 0 for all ij where i is not equal to j and a0] = 1 for all i and j.