Application of Matrices

What is matrix inversion method?

Solve $x-y-1=0, x+z+6=0, x+y-2z=3$ by using determinant.

The sum of three numbers is $6$. If we multiply third number by $3$ and add second number to it, we get $11$. By adding first and third numbers, we get double of the second number. Represent it algebraically and find the numbers using matrix method.

Solve the following system of equations by matrix method:

$$\begin{gathered} 3x-2y+3z=8 \\ 2x+y-z=1 \\ 4x-3y+2z=4 \end{gathered}$$

Solve the system of equations

$\begin{array}{ccccc}2x& +& 5y& =& 1\\ 3x& +& 2y& =& 7\end{array}$

What are the application of matrices?

Solve the following equations using Matrix Inversion method.
$2x+ 3y= 3, 5x+ 4y= 11$

Solve the following equations using Matrix Inversion method.
$x + 2y = 4 , 3x - 5y = 1$

Solve the given system of linear equations using the inverse matrix method.

$2x-y=-5$

$3x+4y=3$

If $x=\alpha ,y=\beta$ and $z=\gamma$ is a solution of the matrix equation $LUX=B$, where

$L=\left[\begin{array}{ccc}1& 0& 0\\ 2& 1& 0\\ 0& -2& 1\end{array}\right],U=\left[\begin{array}{ccc}1& -2& 3\\ 0& -1& 6\\ 0& 0& 2\end{array}\right],X=\left[\begin{array}{l}x\\ y\\ z\end{array}\right]$ and $B=\left[\begin{array}{c}3\\ 11\\ -8\end{array}\right]$

then the sum of $\alpha +\beta +\gamma$ is equal to

If $x=\alpha ,y=\beta$ and $z=\gamma$ is a solution of the system of linear equations

$x-2y+z=0$
$x-y+4z=11$
$x+2y+4z=17$

then the product $\alpha \beta \gamma$ is equal to

A person has $₹30000$ to invest. He wants to invest some amount in the fixed deposit and remaining in savings account. The interest rates are $7\%$ and $5\%$ per annum for the fixed deposit and the saving account respectively. Find how he should divide the total amount $₹30000$ in two accounts if he wants to get the annual interest as $₹2000$.

A person has $₹30000$ to invest. He wants to invest some amount in the fixed deposit and remaining in savings account. The interest rates are $7\%$ and $5\%$ per annum for the fixed deposit and the saving account respectively. Find how he should divide the total amount $₹30000$ in two accounts if he wants to get the annual interest as $₹1800$.

If three numbers are added the sum is $15$. If the second number is subtracted from the sum of first and third number then we get $5$ and If twice the first number is added to the second and the third number is subtracted from the sum we get $4$. Use matrices to find the numbers.

In an election a party hired a firm to promote its candidate in three ways, telephone calls, house calls and letters. The cost per contact (in paise) is respectively $40,100$ and $50$. The number of contacts in cities $A$ and $B$ are $1000,500,5000$ and $3000,1500$ and $7500$ respectively. Express the information using matrices and use the algebra of matrices to get the total amount spent in each city.