Find the Variables

Problem

[[0,3,4],[0,0,3],[0,0,0]]*[[a],[b],[d]]=[[1],[0],[0]]

Solution

1. Perform matrix multiplication on the left side to create a system of linear equations.

0*a+3*b+4*d=1

0*a+0*b+3*d=0

0*a+0*b+0*d=0

2. Simplify the equations to isolate the variables.

3*b+4*d=1

3*d=0

0=0

3. Solve for d using the second equation.

d=0

4. Substitute d=0 into the first equation to solve for b

3*b+4*(0)=1

3*b=1

b=1/3

5. Identify the status of variable a Since a is multiplied by 0 in every equation, it does not affect the equality. Therefore, a can be any real number.

Final Answer

[[a],[b],[d]]=[[a],[1/3],[0]],a∈ℝ

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