Please explain part a,c and d using the answer key I have attached below. Consider the matrices21413-17|1 0370 81-125-3-191-2 0-10 00 00 0A =3-61119.andR =14-1-71-521019.141172340 0ā7 E R° denote the columnsYou may assume that R is the reduced echelon form (RREF) of A. Let ā1,of A, in left-to-right order.....(a) Which of the vectors ā3, ā4, and ā, belong to the span of đ1 and ã2? No justification necessary.(b) What is the largest number of linearly independent vectors that can be chosen from among ả1, .No justification necessary.,ā7?(c) Does āz belong to the span of đ1, ã2, and ā4? If not, explain why not; if so, write āz explicitly as alinear combination of ā1, ã2, and ā4.(d) Are ā1, ā2, ã6, and ā7 linearly independent? If so, explain why; if not, provide a nontrivial lineardependence relation among these four vectors (this means an equation of the formciãi + c2d2 + coã6 + c7ã7with at least one of the coefficients nonzero). For part (a), only đz belongs to span{ã1,ã2}; đ4 and āz do not. For part (b), the largest such number is 4,since the matrix has four pivot columns. For part (c), the answer is yes, āz does belong to span{ā1, ã2, đ4}:an explicit representation is āz = 7ã1 – ã2 + 4ã4. For part (d), the answer is no, ā1, d2, ā6, and ā7 are notlinearly independent. A nontrivial linear dependence relation among them is 8a1 + Oã2 + 9ã6 – ả7 = 0.

The main objective is to solve part a,cand d. In order to solve using the columns of A and using the…

Consider the matrices 0 7 0 8 0 0 0 0 1 4 13 -1 7 1 0 3 1 2 -1 25 -3 -19 1 -2 -1 A = 3 -6 1 1 1 and R = 1 4 -1 2 -7 1 -5 10 0 0 1 9 1 4 1 17 34 You may assume that R is the reduced echelon form (RREF) of A. Let ā1,. of A, in left-to-right order. ..., ā7 E R° denote the columns (a) Which of the vectors ā3, ā4, and āz belong to the span of ā1 and ā2? No justification necessary. (b) What is the largest number of linearly independent vectors that can be chosen from among ā1,. No justification necessary. ,ā7? (c) Does āz belong to the span of ā1, đ2, and ā4? If not, explain why not; if so, write āz explicitly as a linear combination of ā1, ã2, and đ4. (d) Are ā1, ā2, ā6, and ā7 linearly independent? If so, explain why; if not, provide a nontrivial linear dependence relation among these four vectors (this means an equation of the form ciải + c2ã2 + Cóã6 + czā7 = 0 with at least one of the coefficients nonzero).