Which of the given values of x and y make the following pair of matrices equal \(\begin{bmatrix}3x+y&5\\y+1&2-3x\end{bmatrix}=\begin{bmatrix}0&y-2\\8&4\end{bmatrix}\)
\(x=\frac{-1}{3},y=7\)
Not possible to find
\(y=7,x=\frac{-2}{3}\)
\(x=\frac{-1}{3},y=\frac{-2}{3}\)
It is given that \(\begin{bmatrix}3x+y&5\\y+1&2-3x\end{bmatrix}=\begin{bmatrix}0&y-2\\8&4\end{bmatrix}\)
Equating the corresponding elements, we get:
3x+7=0 \(\Rightarrow\)x=\(-\frac{7}{3}\)
5=y-2 \(\Rightarrow\) y=7
y+1=8 \(\Rightarrow\) y=7
2-3x=4 \(\Rightarrow\) x=\(-\frac{2}{3}\)
We find that on comparing the corresponding elements of the two matrices, we get two different values of x, which is not possible.
Hence, it is not possible to find the values of x and y for which the given matrices are equal.
Three students, Neha, Rani, and Sam go to a market to purchase stationery items. Neha buys 4 pens, 3 notepads, and 2 erasers and pays ₹ 60. Rani buys 2 pens, 4 notepads, and 6 erasers for ₹ 90. Sam pays ₹ 70 for 6 pens, 2 notepads, and 3 erasers.
Based upon the above information, answer the following questions:
(i) Form the equations required to solve the problem of finding the price of each item, and express it in the matrix form \( A \mathbf{X} = B \).
A matrix is a rectangular array of numbers, variables, symbols, or expressions that are defined for the operations like subtraction, addition, and multiplications. The size of a matrix is determined by the number of rows and columns in the matrix.