Paper Generator

A shopkeeper sells 50 Chemistry, 60 Physics and 35 Maths books on day I and sells 40 Chemistry, 45 Physics and 50 Maths books on day II. If the selling price for each such subject book is ₹150 (Chemistry), ₹175 (Physics) and ₹180 (Maths), then find his total sale in two days, using matrix method. If cost price of all the books together is ₹35,000, what profit did he earn after the sale of two days?

Let $2x+5y-1=0$ and $3x+2y-7=0$ represent the equations of two lines on which the ants are moving on the ground. Using matrix method, find a point common to the paths of the ants.

If $A=\begin{bmatrix}2&3\\ -1&2\end{bmatrix}$, then show that $A^{2}-4A+7I=0$.

Let $A=\begin{bmatrix}1\\ 4\\ -2\end{bmatrix}$ and $C=\begin{bmatrix}3&4&2\\ 12&16&8\\ -6&-8&-4\end{bmatrix}$ be two matrices. Then, find the matrix B if $AB=C$.

A furniture workshop produces three types of furniture chairs, tables and beds each day. On a particular day the total number of furniture pieces produced is 45. It was also found that production of beds exceeds that of chairs by 8, while the total production of beds and chairs together is twice the production of tables. Determine the units produced of each type of furniture, using matrix method.

If A is a $3\times3$ invertible matrix, show that for any scalar $k\ne0$, $(kA)^{-1}=\frac{1}{k}A^{-1}$. Hence calculate $(3A)^{-1}$, where $A=\begin{bmatrix}2&-1&1\\ -1&2&-1\\ 1&-1&2\end{bmatrix}$.

Let A and B be two square matrices of order 3 such that $\det(A) = 3$ and $\det(B) = -4$. Find the value of $\det(-6AB)$.

If $A=\begin{bmatrix}1&2&0\\ -2&-1&-2\\ 0&-1&1\end{bmatrix}$, then find $A^{-1}$. Hence, solve the system of linear equations: $x-2y=10$, $2x-y-z=8$, $-2y+z=7$.

Given $A=\begin{bmatrix}-4&4&4\\ -7&1&3\\ 5&-3&-1\end{bmatrix}$ and $B=\begin{bmatrix}1&-1&1\\ 1&-2&-2\\ 2&1&3\end{bmatrix}$, find AB. Hence, solve the system of linear equations: $x-y+z=4$, $x-2y-2z=9$, $2x+y+3z=1$.

A school wants to allocate students into three clubs Sports, Music and Drama, under following conditions: The number of students in Sports club should be equal to the sum of the number of students in Music and Drama club. The number of students in Music club should be 20 more than half the number of students in Sports club. The total number of students to be allocated in all three clubs are 180. Find the number of students allocated to different clubs, using matrix method.

Find the product of the matrices $[\begin{bmatrix}1&2&-3\\ 2&3&2\\ 3&-3&-4\end{bmatrix}][\begin{bmatrix}-6&17&13\\ 14&5&-8\\ -15&9&-1\end{bmatrix}]$ and hence solve the system of linear equations: $x+2y-3z=-4$, $2x+3y+2z=2$, $3x-3y-4z=11$

If $A=[\begin{bmatrix}1&2&-3\\ 2&0&-3\\ 1&2&0\end{bmatrix}],$ then find $A^{-1}$ and hence solve the following system of equations: $x+2y-3z=1$, $2x-3z=2$, $x+2y=3$

If $A=[\begin{bmatrix}2&1&-3\\ 3&2&1\\ 1&2&-1\end{bmatrix}],$ find $A^{-1}$ and hence solve the following system of equations: $2x+y-3z=13$, $3x+2y+z=4$, $x+2y-z=8$

If $A=[\begin{bmatrix}-1&a&2\\ 1&2&x\\ 3&1&1\end{bmatrix}]$ and $A^{-1}=[\begin{bmatrix}1&-1&1\\ -8&7&-5\\ b&y&3\end{bmatrix}],$ find the value of $(a+x)-(b+y)$.

If $A=[\begin{bmatrix}1&-2&0\\ 2&-1&-1\\ 0&-2&1\end{bmatrix}],$ find $A^{-1}$ and use it to solve the following system of equations: $x-2y=10$, $2x-y-z=8$, $-2y+z=7$

If $A=\begin{bmatrix}1&cot~x\\ -cot~x&1\end{bmatrix}$ show that $A^{\prime}A^{-1}=\begin{bmatrix}-cos~2x&-sin~2x\\ sin~2x&-cos~2x\end{bmatrix}$

Solve the following system of equations, using matrices: $\frac{2}{x}+\frac{3}{y}+\frac{10}{z}=4$ $\frac{4}{x}-\frac{6}{y}+\frac{5}{z}=1$ , $\frac{6}{x}+\frac{9}{y}-\frac{20}{z}=2$ where x, y, $z\ne0$

If $A=\begin{bmatrix}1&2&-2\\ -1&3&0\\ 0&-2&1\end{bmatrix}$ and $B^{-1}=\begin{bmatrix}3&-1&1\\ -15&6&-5\\ 5&-2&2\end{bmatrix},$ find $(AB)^{-1}$.

OR Solve the following system of equations by matrix method :$ x+2y+3z=6, 2x-y+z=2, 3x+2y-2z=3.$

If $A=\begin{bmatrix}3 & 2\\ 5 & -7\end{bmatrix}$, then find $A^{-1}$ and use it to solve the following system of equations : $3x+5y=11, 2x-7y=-3$.

If $A=\begin{bmatrix}1 & 0 & 2\\ 0 & 2 & 1\\ 2 & 0 & 3\end{bmatrix}$, then show that $A^{3}-6A^{2}+7A+2I=O$