Question

i need help with these two questions. it is from linear algebra

Describe the possible echelon forms of the following matrix. A is a 2x2 matrix with linearly dependent columns. Select all that apply. (Note that leading entries marked with an X may have any nonzero value and starred entries may have any value including zero.) A. Х * B. 0 X 0 0 0 X C. х * D. 0 0 0 0 0 1 5 4 -5 -8 -3 Given A observe that the second column is the sum of the first and third columns. Find a nontrivial -4 -8 -4 5 9 4 solution of Ax 0 without performing row operations. [Hint: Write Ax 0 as a vector equation.] x= LC

Answer 1

A is 2X2 mahix hith lineaely dapndent Columrs dthon ac A = ony Constants a,b,c bc if a=0 and b=0 then A= this is abeady Ja echelon elm -8 1 나 ato Sow opetations echelon fim R2= a R2-bR ac a cchelon m than the us C0 a c uf cto than and D epline thet Satily ale X l

4 -5 3 -8 -4 + -4 - 8 4 5 Jeasiongig 4 -5 -8 3 + -4 -8 -4 5 4 5 = 0 -5 -8 -8 -4 4 -4 5 Ax o Cemfale lith honce LO