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### High School Mathematics11.9 Important Points in Matrices

1. An array of numbers in rows and columns is called a matrix.

2. The numbers arranged in rows and columns in a matrix are called elements of the matrix.

3. [ ] or ( ) is the symbol of a matrix.

4. A matrix having only one row is called a row matrix.

5. A matrix having only column is called a column matrix.

6. A matrix having same number of rows and columns is called a square matrix.

7. A matrix with all its elements as zeros is called a Null matrix or zero matrix and it is represented by '0'.

8. A square matrix in which each of the elements in the principal diagonal is '1 and all other elements are zeros is called an identity matrix or unit matrix.

9. If the rows and columns of a matrix are interchanged, the matrix obtained is called the transpose of the original matrix and is denoted by AT.

10. The number of rows ´ the number of columns of the matrix is called the order of the matrix.

11. Two matrices are equal if the corresponding elements in both the matrices are the same.

12. The multiplication of two matrices A and B is defined if the number of columns in A is equal to the number of rows of B.

13. If a matrix is equal to its transpose it is called a symmetric matrix.

14. If the transpose of a matrix is equal to the additive inverse of the given matrix then the given matrix is called skew symmetric matrix.

15. The diagonal from the first element of the first row to the last element of the last row is called the principal diagonal of square matrix.

16. A square matrix in which all the elements in the principal diagonal are equal and the rest of the elements are zero is called scalar matrix.

17. Solving systems of equations using a variety of methods:
 Method When to use Graphing: Graph each equation in the coordinate plane. The point where the graphs intersect is the solution. The equations have only two variables and are given in a form that is easy to graph. Substitution:Solve one equation for one of the variable and substitute into the other equation(s). One of the variables in the system has a coefficient of 1 or -1. Elimination: Multiply equations by constants, then add the revised equations to eliminate a variable. None of the variables in the system have a coefficient of 1 or -1. Cramer's rule: Use determinants to find the solution. the determinant of the coefficient matrix is not zero. Inverse matrices: Write the system as a matrix equation AX + B. Multiply each side by A-1 on the left to obtain the solution X = A-1B. The determinant of the coefficient matrix is not zero.

 Q 1: If the transpose of a matrix is equal to its additive inverse that matrix is called _______.Skew symmetric matrixSymmetric matrix Q 2: If a matrix A is such that A = AT then A is ______.Skew symmetric matrixSymmetric matrix Q 3: A column matrix is a matrix which has only one _______.ColumnRow Q 4: A zero matrix is a matrix in which every element is ______.OneZero Q 5: In a 3 ´ 2 matrix there are _____ rows.32 Q 6: In a 1 ´ 2 matrix there are ____ columns.21 Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!