Find the Variables [[3,-4,0],[2,8,-1]]+B=[[0,0,0],[0,0,0]]

Problem

[[3,−4,0],[2,8,−1]]+B=[[0,0,0],[0,0,0]]

Solution

1. Identify the matrix equation as A+B=0 where A is the given 2×3 matrix and 0 is the 2×3 zero matrix.

2. Isolate the matrix B by subtracting matrix A from both sides of the equation.

B=[[0,0,0],[0,0,0]]−[[3,−4,0],[2,8,−1]]

3. Perform element-wise subtraction to find the entries of matrix B

B=[[0−3,0−(−4),0−0],[0−2,0−8,0−(−1)]]

4. Simplify the arithmetic for each entry to determine the final matrix.

B=[[−3,4,0],[−2,−8,1]]

Final Answer

[[3,−4,0],[2,8,−1]]+B=[[0,0,0],[0,0,0]]⇒B=[[−3,4,0],[−2,−8,1]]

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