Question - Solving Matrix Equation for Variables
Solution:
The image shows a matrix equation that we need to solve to find the values of p and q. The matrix equation is given as:```[ 4/p p ] [ 7(q) 11(p) ] [-1/q -p ] = [ -3 13 ] ```To solve for p and q, we need to equate elements in the corresponding positions from the given two matrices. That will give us a system of equations as follows:1. (4/p) * 7(q) + p * (-3) = 11(p)2. (-1/q) * 7(q) + (-p) * (-3) = 13Let's solve these equations.For the first equation:(4q/p) * 7 + p * (-3) = 11p28q/p - 3p = 11p28q = 14p^2q = (14p^2)/28q = p^2/2 (1)For the second equation:((-7) + 3p) = 133p - 7 = 133p = 20p = 20/3Now we can substitute the value of p into equation (1) to find q:q = (20/3)^2/2q = 400/9 * 1/2q = 400/18q = 200/9q = 22.222...Therefore, the values of p and q are:p = 20/3q = 200/9However, note that the way both equations are constructed implies that there is an element of matrix multiplication involved, which is not correctly represented in the image. Normally, when multiplying two matrices, the elements are multiplied and then added together according to matrix multiplication rules. The image seems to imply direct multiplication which would defy the matrix multiplication rules. But based on the provided equations and assuming they are correctly representing a matrix product, the above solution for p and q is correct.
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