Question

In: Math

Suppose C is a m × n matrix and A is a n × m matrix....

Suppose C is a m × n matrix and A is a n × m matrix. Assume CA = Im (Im is the m × m identity matrix). Consider the n × m system Ax = b.

1. Show that if this system is consistent then the solution is unique.

2. If C = [0 ?5 1

3 0 ?1]

and A = [2 ?3

1 ?2

6 10] ,,

find x (if it exists) when

(a) b =[1

(b) b =[ 7

22] .

Solutions

Expert Solution

Given, C is a m×n matrix and A is a n×m matrix and CA = I_m, where I_m is the m×m identity matrix.

1) Given system is Ax = b.

Multiplying C on both sides we get, C(Ax) = Cb

i.e., (CA)x = Cb

i.e., x = Cb

Since Cb is an unique mx1 matrix, therefore Ax = b has an unique solution.

Hence, the given consistent system has an unique solution.

2) Given, C = and A =

Now, CA = =

(a) Here b = .

Now, x = Cb

i.e., x =

i.e., x = .

(b) Here x =

Now, x = Cb

i.e., x =

i.e., x = .

milcah answered 1 year ago

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