2 Marks Questions

Question 512 Marks

Find AB, if $A=\left[\begin{array}{ll} {6} & {9} \\ {2} & {3} \end{array}\right] \text { and } B=\left[\begin{array}{lll} {2} & {6} & {0} \\ {7} & {9} & {8} \end{array}\right]$

Answer

Matrix A has 2 columns which is equal to the number of rows of B. Hence AB is defined. Now
$A B=\left[\begin{array}{lll} {6(2)+9(7)} & {6(6)+9(9)} & {6(0)+9(8)} \\ {2(2)+3(7)} & {2(6)+3(9)} & {2(0)+3(8)} \end{array}\right]$
$=\left[\begin{array}{ccc} {12+63} & {36+81} & {0+72} \\ {4+21} & {12+27} & {0+24} \end{array}\right]$
$=\left[\begin{array}{ccc} {75} & {117} & {72} \\ {25} & {39} & {24} \end{array}\right]$

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Question 522 Marks

Consider the following information regarding the number of men and women workers in three factories I, II and III

	Men workers	Women workers
I	30	25
II	25	31
III	27	26

Represent the above information in the form of a 3 $\times$ 2 matrix. What does the entry in the third row and second column represent?

Answer

The information is represented in the form of a 3$\times$2 matrix as follows
$A=\left[\begin{array}{ll} {30} & {25} \\ {25} & {31} \\ {27} & {26} \end{array}\right]$
The entry in the third row and the second column represents the number of women workers in factory III.

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Question 532 Marks

If $A =\left[\begin{array}{rr}8 & 0 \\ 4 & -2 \\ 3 & 6\end{array}\right], B =\left[\begin{array}{rr}2 & -2 \\ 4 & 2 \\ -5 & 1\end{array}\right]$ and $2 A+3 x=5 B$ then find the value of $x$.

Answer

Rearrange the equation for $X: 3 X=5 B-2 A$.
Calculate $5 B: 5\left[\begin{array}{cc}2 & -2 \\ 4 & 2 \\ -5 & 1\end{array}\right]=\left[\begin{array}{cc}10 & -10 \\ 20 & 10 \\ -25 & 5\end{array}\right]$.
Calculate $2 A: 2\left[\begin{array}{cc}8 & 0 \\ 4 & -2 \\ 3 & 6\end{array}\right]=\left[\begin{array}{cc}16 & 0 \\ 8 & -4 \\ 6 & 12\end{array}\right]$.
Subtract: $3 X=\left[\begin{array}{cc}10-16 & -10-0 \\ 20-8 & 10-(-4) \\ -25-6 & 5-12\end{array}\right]=\left[\begin{array}{cc}-6 & -10 \\ 12 & 14 \\ -31 & -7\end{array}\right]$
$X=$ $\frac{1}{3}\left[\begin{array}{cc}-6 & -10 \\ 12 & 14 \\ -31 & -7\end{array}\right]$.

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MATHS 2 Marks Questions