Matrices Question
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Grade 12 Matrices CCSS: HSN-VM.C.10
Sarah has been given the following matrix equation to solve, Ax=b, where A is a 3-by-3 matrix, b is a 3-by-1 matrix, and x is a 3-by-1 matrix. If she knows the equation can be solved by multiplying the inverse of A on both sides of the equation, which of the following must be true?
- A must be a diagonal matrix (its off-diagonal entries must be zero).
- The matrix b must also have an inverse.
- The determinant of A is not equal to zero.
- More than half of the elements in the matrix A are non-zero.