Kay's Math: Matrices - set 1-Practice questions for Bcom Business mathematics syllabus Kerala university

$A= \begin{pmatrix} 2&1 &2 \\ 1&1 &1 \\ 3&2 &1 \end{pmatrix}$ $B= \begin{pmatrix} 12&6 &7 \\ 8&10 &11 \\ 5&6 &12 \end{pmatrix}$ $C= \begin{pmatrix} 0&3 \\ 5&6 \\ 1&1 \end{pmatrix}$ $C= \begin{pmatrix} 8&4 \\ 5&2 \\ 1&3 \end{pmatrix}$

a. Write the order of each of the matrices A, B, C and D
b. Compute A+B , 4A , 3B, 4A+3B
c. Verify whether C and D satisfies commutative law.
d. Is it possible to find the sum of A and C? If no, give reasons.

2.Verify associative law for matrices

$A=\begin{pmatrix} 3&2 &5 \\ 1&2 &2 \end{pmatrix} B= \begin{pmatrix} 1&1&1\\0&0&0\end{pmatrix} C=\begin{pmatrix} 7&3&3\\4&2&1\end{pmatrix}$

3. Commerce department have three sections Tax, CA and MCom. Tax section has three divisions, CA has three and MCom has only two. One division of tax has 23 girls and 45 boys, another 25 girls and 25 boys and last division have 20 girls and 30 boys. First division of CA is filled with 30 girls and 30 boys, second with 45 girls and 2 boys and third have 33 girls and 20 boys. One division of MCom have 12 boys and another 7 boys and 5 girls.

a. Represent the above information in the form of a matrix
b. Find the number of girls in Tax and CA
c. Find the total number of boys in Tax, CA and MCom

4. The wages of an employee for a week are 800,900, 1000, 800, 1000, 900, 1000. Represent the data as matrix. Find the salary for 4 weeks.

5. The matrices A,B,C are defined as follows: $A=\begin{pmatrix} 2&5 \\ 0&1 \end{pmatrix} B= \begin{pmatrix} 1&2&1\\2&0&0\end{pmatrix} C=\begin{pmatrix} 2&2\\0&1\\5&0\end{pmatrix}$
a. Why is AB defined? Why is BA not defined? Calculate AB
b. Why are both BC and CB defined? Is it true that BC=CB?
c.Calculate A(BC) and (AB)C. in general, should the answers be equal?