If: \[ \begin{bmatrix} x + y & 3y \\ 3x + 3 & x + 3 \end{bmatrix} \begin{bmatrix} 9 & x + y \\ 4x + y & y \end{bmatrix} \] then \( (x - y) = ? \)

Question

Let the foot of the perpendicular from the point \( (1, 2, 4) \) on the line \( \frac{x+2}{4} = \frac{y-1}{2} = \frac{z+1}{3} \) be \( P \). Then the distance of \( P \) from the plane \( 3x + 4y + 12z + 23 = 0 \) is:

Answer 1

We are given the matrix multiplication:\[ \begin{bmatrix} x + y & 3y\\ 3x + 3 & x + 3 \end{bmatrix} \begin{bmatrix} 9 & x + y \\ 4x + y & y \end{bmatrix}\]Multiplying the matrices step-by-step and equating the results yields an equation in \( x \) and \( y \). Solving this equation allows us to determine the value of \( (x - y) \). The calculated value of \( (x - y) \) is \( -3 \).

If: \[ \begin{bmatrix} x + y & 3y \\ 3x + 3 & x + 3 \end{bmatrix} \begin{bmatrix} 9 & x + y \\ 4x + y & y \end{bmatrix} \] then \( (x - y) = ? \)

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Solution and Explanation

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