Let C = .|a b| |c d| |e f| (a) What is the biggest possible value of rank(C)? (b

Question

Let C = .|a b|
|c d|
|e f|

(a) What is the biggest possible value of rank(C)?

(b) What is the smallest possible of rank(C)?

(c) If C is the coefficient matrix of a homogeneous linear system:

(i) What is the least number of solutions the system can have?

(ii) What is the biggest number of solutions the system can have?

(iii) Can the system have exactly three solutions?

(d) Redo part (c) if C is the matrix of a non-homogeneous linear system.

(e) Redo parts (a)-(d) for the matrix D = | a b c|
|d e f|

Explanation / Answer

order of C = 3x2 a) highest rank = 2 b) lowest rank = 1 c) i) zero (No soultion) ii) Infinite solutions iii) No, because there's only two independent variables order of C=2x3 a) highest rank=2 b ) lowst rank=1 c) i) zero (No soultion) ii) Infinite solutions iii) No, THere's 3 independent variables and only two equatio...

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