Simplify the Matrix

Problem

[[7*x,3*y,−1*z,−1*w,1],[1*x,−1*y,1*z,3*w,2],[9*x,−1*y,−1*z,0,6],[1*x,1*y,0,0,−3]]

Solution

1. Identify the components of the matrix. Each entry consists of a coefficient multiplied by a variable (x,y,z,w or a constant.

2. Simplify the notation by removing unnecessary coefficients of 1 and −1 and removing the variable labels if the task implies converting to an augmented matrix or a coefficient matrix.

3. Rewrite the terms 1*x as x −1*y as −y −1*z as −z and −1*w as −w to follow standard algebraic conventions.

4. Present the matrix in its cleanest algebraic form.

Final Answer

[[7*x,3*y,−z,−w,1],[x,−y,z,3*w,2],[9*x,−y,−z,0,6],[x,y,0,0,−3]]

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