what is the order of the operations for the following equation, where $A$ is a matrix, $I$ is an identity matrix and $K$ is a scalar?
$$A^3 - 6A^2 + 7A + KI = 0$$
Do I have to 2nd and 3rd terms first and subtract it from the 1st term or vice-versa?
2026-05-06 05:10:54.1778044254
order of operations in matrices
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1
The order would be the same as if you are calculating the value $x^3-6x^2+7x+k\cdot 1$ except you are dealing with a matrix, not a number:
$$(A^3) - (6\cdot(A^2)) + (7\cdot A) + (K\cdot I)$$
The order in which you calculate the summation is irrelevant, because addition of matrices is both associative and commutative. The way you calculate $A^3$ (either $A\cdot(A\cdot A)$ or $(A\cdot A)\cdot A$) also has no effect on the final result, because matrix multiplication is associative.