Name: The Applications of Matrices
Uploaded: 2019-07-19
Duration: 7 min 47 s
Description: Let's learn the applications of matrices, such as solving homogenous and non-homogenous linear equations, the Gauss-Jordan method, and the reduction method.

Question

The sum of the costs of one book each of Mathematics, Physics and Chemistry is .

₹ 210

. Total cost of a mathematics book, 2 physics books, and a chemistry book is

₹

240 / -

Also the total cost of a Mathematics book,

3

physics book and chemistry books is

₹ 300 / -

. Find the cost of each book, using Matrices.

Accepted Answer

Let, cost of $1$ Mathematics book, $1$ Physics book and $1$ Chemistry book are $₹ x, ₹ y$ and $₹ z$ .

The system of linear equations are

$∴ x + y + z = 210 - - - - (i) x + 2 y + z = 240 - - - (ii) x + 3 y + z = 300 - - - (iii)$

The matrix representation of the equations is

$[\begin{matrix} 1 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 3 & 1 \end{matrix}] [\begin{matrix} x \\ y \\ z \end{matrix}] = [\begin{matrix} 210 \\ 240 \\ 300 \end{matrix}]$

$R_{2} \to R_{2} - R_{1}$ and $R_{3} = R_{3} - R_{1}$ , we get

$[\begin{matrix} 1 & 1 & 1 \\ 0 & 1 & 0 \\ 0 & 2 & 1 \end{matrix}] [\begin{matrix} x \\ y \\ z \end{matrix}] = [\begin{matrix} 210 \\ 30 \\ 90 \end{matrix}]$

$R_{3} = R_{3} - 2 R_{2}$ , we get

$[\begin{matrix} 1 & 1 & 1 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}] [\begin{matrix} x \\ y \\ z \end{matrix}] = [\begin{matrix} 210 \\ 30 \\ 30 \end{matrix}]$

$∴ x + y + z = 210 - - - - (iv) y = 30 - - - (v) z = 30 - - - (vi)$

From $(v)$ and $(vi)$ ;

$y = 30$ and $z = 30$ .

Substituting $y = 30$ and $z = 30$ in eqn $(iv)$ , we get

$x + 30 + 30 = 210 \Rightarrow x + 60 = 210 \Rightarrow x = 150$

The cost of Mathematics, Physics and Chemistry book are $₹ 150, ₹ 30$ and $₹ 30$ respectively.

Important Questions on Matrices

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