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Find x and y. 5(1/0 2/-1) - (w/y x/z) = 3(3/-1 4/7) Find p and q. 3(p/4 5/8) - (-2/0 7/2) = 2(-5/6 4/q)

Mathematics

ScanSolve AI Answer

Answer

x=−2,y=3x = -2, y = 3

Step-by-step solution

3 steps

Here's how to solve :

  1. Perform the scalar multiplication on both sides of the matrix equation.

    5(120−1)−(wxyz)=3(34−17)5\begin{pmatrix} 1 & 2 \\ 0 & -1 \end{pmatrix} - \begin{pmatrix} w & x \\ y & z \end{pmatrix} = 3\begin{pmatrix} 3 & 4 \\ -1 & 7 \end{pmatrix} (5×15×25×05×(−1))−(wxyz)=(3×33×43×(−1)3×7)\begin{pmatrix} 5 \times 1 & 5 \times 2 \\ 5 \times 0 & 5 \times (-1) \end{pmatrix} - \begin{pmatrix} w & x \\ y & z \end{pmatrix} = \begin{pmatrix} 3 \times 3 & 3 \times 4 \\ 3 \times (-1) & 3 \times 7 \end{pmatrix} (5100−5)−(wxyz)=(912−321)\begin{pmatrix} 5 & 10 \\ 0 & -5 \end{pmatrix} - \begin{pmatrix} w & x \\ y & z \end{pmatrix} = \begin{pmatrix} 9 & 12 \\ -3 & 21 \end{pmatrix}
  2. Equate the corresponding elements to form equations for xx and yy.

    For xx, we look at the element in the first row, second column:

    10−x=1210 - x = 12

    For yy, we look at the element in the second row, first column:

    0−y=−30 - y = -3
  3. Solve the equations for xx and yy.

    For xx:

    10−x=1210 - x = 12 −x=12−10-x = 12 - 10 −x=2-x = 2 x=−2x = -2

    For yy:

    0−y=−30 - y = -3 −y=−3-y = -3 y=3y = 3

    The values are x=−2x = -2 and y=3y = 3.

    x=−2,y=3x = -2, y = 3
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