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3. Define a linear transformation h : R3 → R3. The matrix representation of h over standard bases is given by -2 H= - 8
Posted: Thu May 12, 2022 1:07 pm
by answerhappygod
- 3 Define A Linear Transformation H R3 R3 The Matrix Representation Of H Over Standard Bases Is Given By 2 H 8 1 (55.96 KiB) Viewed 31 times
3. Define a linear transformation h : R3 → R3. The matrix representation of h over standard bases is given by -2 H= - 8 0 1 -3 5 1 2 4 (a) [3 points) Write out the formula of h, i.e., find out the expression of h( B) y Z ). (b) [8 points] Determine the column space and null space of matrix H (i.e. Col(H) and Nul(H)) and the dimensions of Col(H) and Nul(H), respectively. (c) [9 points) Given vectors V1, V2,V3 E R3. It is known that h(v1 + 2v2 + 3v3) = 16 6 25 h(4v1 + 8V2 + 0v3) = -12 16 Find out all possible V3 satisfying the above two equations.