What would you like to understand?

In this context, $A \circ B$ denotes the transformation obtained by applying B first and then applying A to the result. The notation follows the convention where the rightmost transformation acts first on the input vector.

Conditions: A and B are treated as transformations on the same space, here three-dimensional space.; The output of B must be an input acceptable to A.

In this context, $A \circ B$ denotes the transformation obtained by applying B first and then applying A to the result. The notation follows the convention where the rightmost transformation acts first on the input vector.

Conditions: A and B are treated as transformations on the same space, here three-dimensional space.; The output of B must be an input acceptable to A.

When computing the composition $A \circ B$, the matrix B represents the first transformation. Its columns are the images of the standard basis vectors under B.

Conditions: A and B are 3x3 matrices representing linear transformations.; The goal is to find the matrix representation of the composite transformation.

When computing the composition $A \circ B$, the matrix B represents the first transformation. Its columns are the images of the standard basis vectors under B.

Conditions: A and B are 3x3 matrices representing linear transformations.; The goal is to find the matrix representation of the composite transformation.