Answer

Verified

413.4k+ views

**Hint:**Assume investment on one of the bonds as a variable. Then you automatically get the investment on the second bond. After that form two matrices one for investments and one for interests per year. At last, get the annual interest and equate it to the value given in the question.

**Complete step-by-step answer:**

Let the investment on first bond be Rs $x$

Total investment$ = $Rs$30,000$

Investment on second bond$ = $Rs$\left( {30,000 - x} \right)$

Now let us represent investment per bond by the matrix $A$

$A = \left[ {\begin{array}{*{20}{c}}

x \\

{30000 - x}

\end{array}} \right]$

$A$ is a $2 \times 1$ matrix which means it has $2$ rows and $1$ columns.

Now we will represent interest per year by a matrix.

Interest paid by the first bond$ = 5\% $

Interest paid by the second bond$ = 7\% $.

$B = \left[ {\begin{array}{*{20}{c}}

{5\% }&{7\% }

\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}

{\dfrac{5}{{100}}}&{\dfrac{7}{{100}}}

\end{array}} \right]$

$B$ is the $1 \times 2$ matrix which means it has $1$ row and 2 columns.

Now the question arises why we took $B$ as the $1 \times 2$ matrix and not $2 \times 1$ like $A$

This answer is to the fact that matrix multiplication takes place only when the number of columns of the first matrix is equal to the number of rows of the second matrix.

As it is said that we have to solve it by matrix multiplication, therefore it is necessary to take the order of matrices $A$ and $B$ in such a way that matrix multiplication is possible.

Now total annual interest$ = $ interest per bond $ \times $ investment per bond

$1800 = {\left[ {\begin{array}{*{20}{c}}

{\dfrac{5}{{100}}}&{\dfrac{7}{{100}}}

\end{array}} \right]_{1 \times 2}} \times {\left[ {\begin{array}{*{20}{c}}

x \\

{30000 - x}

\end{array}} \right]_{2 \times 1}}$

$ = {\left[ {\dfrac{{5x}}{{100}} + \dfrac{7}{{100}}\left( {30000 - x} \right)} \right]_{1 \times 1}}$

$ = \dfrac{{5x + 21000 - 7x}}{{100}}$

$180000 = 210000 - 2x$

$2x = 30000$

$x = 15000$

Hence amount invested at $5\% = $ Rs$15000$

Amount invested at $7\% =$Rs$\left( {30,000 - x} \right)$= $ Rs$15000

**Note:**The most important part about this question is to choose the order of the matrix for matrix multiplication. Students choose the wrong order of the matrix and are not able to multiply the matrices or multiply them in the wrong way.

Also it should be known to you that:

Total annual interest $ = $ Interest $ \times $ investment.

Recently Updated Pages

Identify the type of clause underlined in the sentence class 8 english CBSE

Which statement describes the density of the inner class 8 social science CBSE

Babur considered which ruler of Gujarat as among the class 8 social science CBSE

Which island groups were affected by the Tsunami in class 8 social science CBSE

Which is the administrative system that works under class 8 social science CBSE

The year in which the state was named as Karnataka class 8 social science CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

List some examples of Rabi and Kharif crops class 8 biology CBSE

Which are the Top 10 Largest Countries of the World?

The provincial president of the constituent assembly class 11 social science CBSE

Write the 6 fundamental rights of India and explain in detail