The steps shown can be used to prove that the medians of a triangle meet at a point. 1. define segments bd and ce as medians of triangle abc. 2. write linear equations for and . 3. use a system of linear equations to solve for the coordinates of intersection point g. 4. write the equation of . 5. write an expression for the midpoint of bc, point f. 6. ?

1 step. Let ABC be a triangle with vertices

Define segments BD and CE as medians of triangle ABC.

2 step. Write linear equation for medians BD and CE:

3 step. Solve the system of equations:

4 step. Write an equation for AO, where O is the point of intersection BD and CE.

5 step. Write an expression for the midpoint of BC, point F:

6 step. Check that coordinates of point F satisfy the equation of AO (then f lies on AO and AO is the third median, that means that all three medians intersect in one point).

Simplify it and get 1=1. This means that point F lies on AO.

solution:

→c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.

that is, number of columns of a= number of rows of b.

so, size of matrix , c= a b is , if a = (m × n)matrix

b= (n × p)matrix

then a b = [ (m × n)matrix] ×[   (n × p)matrix ]

→→c= a b= [m × p ] matrix

→→size of product a b will be equal to = number of rows of a × number of columns of b