True or false? , is a linear mapping. Why?

Answer. True if and only if . Verify linearity

True or False? The 3x2 real-component matrix can have maximal rank .

Answer. True. Since and can have at most two linearly independent column vectors, e.g.,

True or false? is an element of ,

Explain.

Answer(s). False. Applying convention of column organization of vector components,

Imposing leads to third-component equation

contradiction.

False. is shown as a row vector.

True or false? It is known that and . Then . Explain. Answer. Ambigous. Subtracting equations gives , hence . If then . If then .

True or False? for

Answer. False. Compute