Let M be any 3 x 3 matrix with entries from the set {0,1, 2}.The maximum number of such matrices. For which the sum of diagonal elements of MTM is seven, is

# Let M be any 3 x 3 matrix with entries from the set {0,1, 2}.The maximum number of such matrices. For which the sum of diagonal elements of MTM is seven, is

Fill Out the Form for Expert Academic Guidance!l

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

### Solution:

${\mathrm{M}}^{\mathrm{T}}\mathrm{M}=\left[\begin{array}{l}\mathrm{a} \mathrm{b} \mathrm{c}\\ \mathrm{d} \mathrm{e} \mathrm{f}\\ \mathrm{g} \mathrm{h} \mathrm{i}\end{array}\right]\left[\begin{array}{l}\mathrm{a} \mathrm{d} \mathrm{g}\\ \mathrm{b} \mathrm{e} \mathrm{h}\\ \mathrm{c} \mathrm{f} \mathrm{i}\end{array}\right]={\mathrm{a}}^{2}+{\mathrm{b}}^{2}+{\mathrm{c}}^{2}+{\mathrm{d}}^{2}+{\mathrm{e}}^{2}+{\mathrm{f}}^{2}+{\mathrm{g}}^{2}+{\mathrm{h}}^{2}+{\mathrm{i}}^{2}=7$
Case I: Seven (1’s) and two (0’s)Number of matrices$=\frac{9!}{7!2!}=36$
Case II : One (1) and three (2’s) and five (0’s)Number of matrices $=\frac{9!}{5!3!}=504$
$\therefore$Total number of matrices = 540

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)