Answer to Question #98549 in Algebra for Shaheli Chattopadhyay

Question

3. (a) A coach buys 3 cricket bats and 6 balls for
3,900. Later, he buys 1 bat and 3 balls for
another team for 1,450. Write two linear
equations to represent the purchases. Why
can the linear system so obtained be solved
by Cramer's rule ? Also, use the rule to
solve the system, and interpret the solution
in the given context. 4
(b) Give an example of a 4 x 1 matrix with
entries from Z \ N.

Answer 1

3 (a). 3x+6y=3900

x+3y=1450

$$\Delta=\begin{vmatrix} 3 & 6 \\ 1 & 3 \end{vmatrix}=9-6=3$$

is not equal to zero;

$$\Delta x=\begin{vmatrix} 3900& 6 \\ 1450 & 3 \end{vmatrix}=3900*3-1450*6=3000$$

$$\Delta y=\begin{vmatrix} 3 & 3900 \\ 1 & 1450 \end{vmatrix}=3*1450-1*3900=450$$

$$x=\Delta x/\Delta=3000/3=1000$$

$$y=\Delta y/ \Delta=450/3=150$$

x stands for bats, y stands for balls.

4 (b).

$A=\begin{bmatrix} -1 \\ -2 \\ -3 \\ -4 \end{bmatrix}$