Question

4xy + 5ax2- 2ay +5x4 + 2xs 2x4+2xs 4x4 +x = 0 in ce 2x3- 9. (a) 2x, +2x- 4a x a + 2ax3 + 4x4 + -2x1 4a7 +8x3 + 10x4 +xs = 0 6. (a) Does Theorem 1 imply that the s- 3y 0 has nontrivial system 2x- 6y = 0 solutions? Explain. (b) Show that the converse to Theorem 1 is not true. That is, show that the existence of nontrivial solutions does not imply that there are more variables than equations. 10. 7. In each case determine how many solutions (and how many parameters) are possible for a homogeneous system of four linear equations in six variables with augmented matrix A. Assume that A has nonzero entries. Give all possibilities. (a) Rank A = 2 .(b) Rank A =1 (c) A has a row of zeros. (d) The row-echelon form of A has a row of zeros. An Application SECTION 1.4 There are many tvnes of

could you please help me with understanding why the answer to d) is not 3 parameters but instead 5,4 or 3? In a row echelon form, don’t we know that each non-zero rows has a leading 1 (by definition)? And so we know that the rank must be 3? 6-3=3 (by given theorem: n-r= #parameter)

Answer 1

sd Givey 1t22-273-2 250 241+22-473- 494 O 1-224273 44yta0 Tn matein fom 6 2 L2-2 I 2 -2 -y 8 10 K3- R3-P puRetay -2 2 1 1 -3 0 o 0-2 4 6 -2 2 2 13 -3 4 6 2 0 O 2 2-2 -3 y 6 2 Rank Augmented malta- 6.(n) mater -3 Ran e non gero n-o Rank t matea Rank