Find the Variables [[0,-2],[0,0]][[x],[y]]=[[1],[0]]

Problem

[[0,−2],[0,0]]*[[x],[y]]=[[1],[0]]

Solution

1. Perform matrix multiplication on the left side of the equation by multiplying the rows of the first matrix by the column vector.

0*(x)+(−2)*(y)=1

0*(x)+0*(y)=0

2. Simplify the equations resulting from the multiplication to isolate the variables.

−2*y=1

0=0

3. Solve for y by dividing both sides of the first equation by −2

y=−1/2

4. Analyze the variable x by looking at the simplified system. Since x is multiplied by 0 in both equations, its value does not affect the equality.

x∈ℝ

Final Answer

[[0,−2],[0,0]]*[[x],[y]]=[[1],[0]]⇒x∈ℝ,y=−1/2

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