Maharashtra Board Solutions for Chapter: Matrices, Exercise 5: Miscellaneous Exercise 2(B)

For a $2\times 2$ matrix $A$, if $A\left(adjA\right)=\left[\begin{array}{cc}10& 0\\ 0& 10\end{array}\right]$ then determinant A equals

If $A^{\text{'}}=-\frac{1}{2}\left[\begin{array}{cc}1& -4\\ -1& 2\end{array}\right]$ then $A=$

Solve the following equations by the methods of inversion $2x-y=-2, x+5y=5$

Solve the following equations by the methods of inversion $x+y+z=-1, y+z=2$ and $x+y-z=3$

The cost of $4$ pencils, $3$ pens and $2$ books is Rs.$150$. The cost of $1$ pencil,$2$ pens and $3$ books is Rs.$125$. The cos of 6 pencils, $2$ pens and $3$ books is Rs.$175$. Find the cost of each item by using Matrices.

The sum of three numbers is $6$. Thrice the third number when added to the first number gives $7$.

On adding three times first number to the sum of second and third number we get $12$. Find the three numbers by using Matrices.

An amount of  $₹5000$ is invested in three types of investments, at interest rates $6.7,7.7,8\%$ per annum respectively. The total annual income from these investment is$₹350 /-$ If the total annual income from first two investment is$₹70$ more than the income from the third, find the amount of each investment using matrix method.

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.