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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 0
Posted: Tue May 10, 2022 6:26 am
by answerhappygod
- 3 Define A Linear Transformation H R3 R3 The Matrix Representation Of H Over Standard Bases Is Given By 2 H 8 0 1 (225.72 KiB) Viewed 21 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| 1). 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) 4 -12 16 Find out all possible V3 satisfying the above two equations.