Spreadsheet #22:  More Matrix Operations - Titanium and Vanadium in Steel

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After an inverted matrix is calculated for a series of standard solutions, it may be used over and over to find the solutions to multiple samples in the same series of samples.  For example, Ti and V both exhibit absorbance at 400 and 460 nm.   However, knowing their absorbtivity coefficients at these wavelengths allows the calculation of an inverted matrix.  Then, absorbences at both wavelengths may be multiplied by the inverted matrix to obtain the desired concentrations of Ti and V. 

From the data in the table below, calculate the inverted matrix and then determine [Ti] and [V] for each of the six samples.  (Click to download data: 22-Ti&V)

Spreadsheet #22 - Titanium and Vanadium in Steel
.	(µg/mL Abs.Coef'.s)		.	.	.	.
Wavelength	Ti	V		Inverted Matrix:
400nm	0.269	0.057		.	.	.
460nm	0.134	0.091		.	.
Sample#:	1	2	3	4	5	6
Abs @400nm:	0.172	0.366	0.370	0.640	0.902	0.600
Abs @460nm:	0.116	0.430	0.298	0.436	0.570	0.660
[Ti] (µg/mL) =	.	.	.	.	.	.
[V] (µg/mL) =	.	.	.	.	.	.