4. Let W be the subspace of R3 spannexl by w1f⎝⎛2/31/32/3⎠⎞ and w2−⎝⎛−2/32/31/3⎠⎞. Which of the following is the
Posted: Thu Jul 14, 2022 3:57 pm
4. Let W be the subspace of R3 spannexl by w1f⎝⎛2/31/32/3⎠⎞ and w2−⎝⎛−2/32/31/3⎠⎞. Which of the following is the orthogonal projection of ⎝⎛111⎠⎞ onto W (a) 91⎝⎛8711⎠⎞ (b) 91⎝⎛−8711⎠⎞ (c) 91⎝⎛7811⎠⎞ (d) 91⎝⎛−78−11⎠⎞ 5. Let W be a subspace of it 10- dimerisional inner produd sface V. If dimW−6, what is dimW1 ? (a) 6 (b) 5 (c) 1 (d) 10 6. Let L:R3→R2[x] be a lincar transformation such that L⎝⎛100⎠⎞−x+x2,L⎝⎛010⎠⎞−1+x and L⎝⎛001⎠⎞−1+x2. Calculate L⎝⎛23−1⎠⎞. (a) x2−5x+1 (b) x2+5x+2 (c) x2+12x−5 (d) x2+2x+5