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(4) Suppose the following matrix B is the echelon form of a matrix A: 24 01 00 00 Answer the following questions with reasons. The word 'plane" is

Please help me to solve the whole question. (a) What are the solutions of Ax = 0? (b) Before you knew B, how many planes in which dimensional space were intersecting to give the solution space of Ax = 0? (c) Looking at B, how many planes do you minimally need to cut out the solution space of Ax = 0? (d) Write down a new plane which when added to Bx = 0 will make the system inconsistent. (e) Are the columns of A linearly independent? (f) Find smallest number of vectors so that they along with the columns of B will

WechatIMG103.jpeg

WechatIMG103.jpeg

(4) Suppose the following matrix B is the echelon form of a matrix A: 24
01
00
00 Answer the following questions with reasons. The word ‘plane” is being used
below to mean planes of any dimension.
(a) What are the solutions of Ar = 0? B: (b) Before you knew 5’, how many planes in which dimensional space were
intersecting to give the solution space of Ax = 0'? (c) Looking at B. how many planes do you minimally need to cut out the solution
space of Ar = 0? (d) Write down a new plane which when added to BJ: = 0 will make the system
inconsistent. (e) Are the columns of A linearly independent? (f) Find smallest number of vectors so that they along with the columns of B will
span R‘.

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