Thread: Matrix Algebra.

Hey everyone,

Could someone please shine some light on this question, I'm not sure I fully understand how it's worded?

Chris.


A range of metallic alloys are tested for electrical conductivity and give the following results for identically sized samples.

25% copper with 75% tin gave a reading of 0.0071 Ohms
65% copper with 35% cadmium gave a reading of 0.0049 Ohms
40% copper with 40% tin and 20% cadmium gave a reading of 0.0060 Ohms

Using matrix algebra, determine the resistance of an equally sized sample for each of the pure metals –

(a) Copper
(b) Tin
(c) Cadmium

Originally Posted by ckeller

Hey everyone,

Could someone please shine some light on this question, I'm not sure I fully understand how it's worded?

Chris.


A range of metallic alloys are tested for electrical conductivity and give the following results for identically sized samples.

25% copper with 75% tin gave a reading of 0.0071 Ohms
65% copper with 35% cadmium gave a reading of 0.0049 Ohms
40% copper with 40% tin and 20% cadmium gave a reading of 0.0060 Ohms

Using matrix algebra, determine the resistance of an equally sized sample for each of the pure metals –

(a) Copper
(b) Tin
(c) Cadmium

let [A] be a 3x3 matrix with percentages of copper, tin, and cadmium for each alloy

let [B] be a 3x1 matrix of the unknown resistances of each individual metal

let [C] be a 3x1 matrix of the measured resistance of each alloy

[A][B] = [C]

solve for matrix [B]

My calculator sez the resistances for copper, tin, and cadmium to be .0056, .0076, and .0036 ohms respectively.

Originally Posted by skeeter

let [A] be a 3x3 matrix with percentages of copper, tin, and cadmium for each alloy

let [B] be a 3x1 matrix of the unknown resistances of each individual metal

let [C] be a 3x1 matrix of the measured resistance of each alloy

[A][B] = [C]

solve for matrix [B]

My calculator sez the resistances for copper, tin, and cadmium to be .0056, .0076, and .0036 ohms respectively.

Hey Thanks very much for your reply it makes sense now.. although I have derived the same but smaller... 0.000056, 0.000076, and 0.000036...

I wonder where I went wrong there

Originally Posted by ckeller

Hey Thanks very much for your reply it makes sense now.. although I have derived the same but smaller... 0.000056, 0.000076, and 0.000036...

I wonder where I went wrong there

I suspect you failed to represent the given percentages as their decimal equivalents.

Originally Posted by skeeter

I suspect you failed to represent the given percentages as their decimal equivalents.

Hey yeah I realized that just as I posted my last comment, silly me lol

Thanks for your help.