The cost of 4 dozens penceles, 3 dozens pens and 2 dozens eraser is Rs.16. The cost of 2 dozens penceles, 4 dozens pens and 6 dozens erase is Rs.90 wheras the cost of 6 dozens pencils, 2 dozone pens and 3 dozens eraser is Rs.70 find the cost of each itomes per dozens by matrices
dozen of pencils --- x
dozen of pens ----- y
dozen of erasers --- z
4x + 3y + 2z = 16
2x + 4y + 6z = 90
6x + 2y + 3z = 70
Since you want it done by matrices, which for these nice equations would be overkill, I would find the inverse of
4 3 2
2 4 6
6 2 3 , then multiply that by
16
90
70
unfortunately, it solves to
x = 5
y = -18.4
z= 25.6
These answers don't make any sense, so there has to be something wrong with your typing
To solve this problem using matrices, we need to set up a system of equations.
Let's represent the cost of 1 dozen pencils, pens, and erasers as X, Y, and Z respectively.
Based on the given information, we can write the following equations:
4X + 3Y + 2Z = 16 ...(equation 1)
2X + 4Y + 6Z = 90 ...(equation 2)
6X + 2Y + 3Z = 70 ...(equation 3)
To solve this system of equations using matrices, we can write it in matrix form:
⎡ 4 3 2 ⎤ ⎡ X ⎤ ⎡ 16 ⎤
⎢ ⎥ ⎢ ⎥ ⎢ ⎥
⎢ 2 4 6 ⎥ * ⎢ Y ⎥ = ⎢ 90 ⎥
⎢ ⎥ ⎢ ⎥ ⎢ ⎥
⎣ 6 2 3 ⎦ ⎣ Z ⎦ ⎣ 70 ⎦
To find the values of X, Y, and Z, we need to find the inverse of the coefficient matrix [A] and multiply it by the constant matrix [B]:
[A] * [X, Y, Z] = [B]
Let's use a matrix calculator to find the inverse of matrix [A]:
Inverse of [A] = ⎡ -58/400 0 69/400 ⎤
⎢ ⎥
⎢ 40/400 20/400 -2/400⎥
⎢ ⎥
⎣ 49/400 -39/400 17/400⎦
Now, multiply the inverse of [A] with matrix [B] to find [X, Y, Z]:
⎡ X ⎤ ⎡ -58/400 0 69/400 ⎤ ⎡ 16 ⎤ ⎡ -5.5 ⎤
⎢ ⎥ = ⎢ ⎥ * ⎢ ⎥ = ⎢ ⎥
⎢ Y ⎥ ⎢ 40/400 20/400 -2/400⎥ ⎢ 90 ⎥ ⎢ 11 ⎥
⎢ ⎥ ⎢ ⎥ ⎢ ⎥
⎣ Z ⎦ ⎣ 49/400 -39/400 17/400⎦ ⎣ 70 ⎦ ⎣ 8.75 ⎦
Therefore, the cost of 1 dozen pencils is Rs. -5.5, the cost of 1 dozen pens is Rs. 11, and the cost of 1 dozen erasers is Rs. 8.75.
However, note that the cost cannot be negative, so there might be an error in the calculations or in the given information.