Linear algebra and probability 2
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Consider the matrix

Find A−1 .

Solve the system

Write the matrix
⎡ ⎤ −10 ⎣ 3 ⎦ 14
as a linear combination of the matrices
Question 2. Let V be the vector space of polynomials with degree ≤ 3, and
a linear combination of p1, p2, and p3? If yes, write p as a linear combination of p1, p2, and p3. If not, explain why not.
a linear combination of p1, p2, and p3? If yes, write p as a linear combination of p1, p2, and p3. If not, explain why not.

Are the vectors p1, p2, p3 linearly independent?

Does the set {p1, p2, p3} span V ?

Is the set {p1, p2, p3} a basis of V ?
Question 3. Let V be the set of 2×1 matrices, and deﬁne a mapping F : V → V by matrix multiplication:

Is F a linear mapping? Justify your answer.

Is F a onetoone mapping? Justify your answer.

Is F an onto mapping? Justify your answer.

Does F have an inverse? If yes, ﬁnd the inverse. If not, explain why not.