Linear algebra and probability 2

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  • Consider the matrix

  • Find A1 .

  • 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 one-to-one 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.