<prompt> Acha mathbfv_0 iwe vekta. Vekta mathbfv_0 inakadiriwa kwenye beginpmatrix 3 1 endpmatrix, na kusababisha vekta mathbfv_1. Vekta mathbfv _1 kisha inakadiriwa kwenye beginpmatrix 1 1 endpmatrix, na kusababisha vekta mathbfv_2. Tafuta matrix ambayo inachukua mathbfv_0 hadi mathbfv_2.  <response>: Matrix ambayo inaangazia beginpmatrix 3 1 endpmatrix nianzapmatrix frac910 frac310 frac310 frac110 endpmatrix, na matrix ambayo inaangazia beginpmatrix 1 1 endpmatrix nianzapmatrix frac12 frac12 frac12 frac12 endpmatrix, kwa hivyo matrix inayochukua mathbfv_0 hadi mathbfv_2 nianzapmatrix frac12 frac12 frac12 frac12 endpmatrix anza pmatrix frac910 frac310 frac310 frac110 endpmatrix beginpmatrix frac35 frac15 frac35 frac15 endpmatrix. 