Chapter 5 - Inner Product Spaces - 5.3 The Gram-Schmidt Process - True-False Review - Page 365: e

False

If $B_1=\{x_1,x_2\}\\ B_2=\{y_1,y_2\}$ Apply Gram- Schmidt process: $v_1=x_1\\ v_2=x_2-\frac{}{||v_1||^2}v_1$ and $v_1=y_1\\ v_2=y_2-\frac{}{||v_1||}^2v_1$ hence $x_2-\frac{}{||v_1||^2}v_1=y_2-\frac{}{||v_1||^2}v_1\\ x_2-\frac{}{||v_1||^2}x_1=y_2-\frac{}{||v_1||^2}x_1$ This does not mean that $x_2=y_2$