# Show that AB is a zero matrix, provided θ − ϕ is an odd multiple of π over 2

## Chapter 3 Matrices Class 12 Maths

**Question 7. **If {\displaystyle A = { \begin{bmatrix} {\cos^2\theta} & {\cos \theta \sin \theta} \\ {\cos \theta \sin \theta } & {\sin^2 \theta} \end{bmatrix} } } , {\displaystyle B = {\begin{bmatrix} {\cos^2 \phi} & { \cos \phi \sin \phi } \\ {\cos \phi \sin \phi } & {\sin^2 \phi } \end{bmatrix}} } then show that AB is a zero matrix, provided {\displaystyle (\theta - \phi )} is an odd multiple of {\displaystyle \frac{\pi }{2}} .

## Express the following matrices as the sum of symmetric and a skew symmetric matrix

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October 2, 2022, 10:23 pm

Question 4. Express the following matrices as the sum of symmetric and a skew symmetric matrix: {\displaystyle {\begin{bmatrix} 2&{ - 2}&{ - 4}\\ { - 1}&3&4\\ 1&{ - 2}&{ - 3} \end{bmatrix}} }

## Show that the matrix B′AB is symmetric or skew symmetric according

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November 1, 2022, 5:14 am

NCERT Miscellaneous Exercise Question 5 : Show that the matrix B′AB is symmetric or skew symmetric according as A is symmetric or skew symmetric.

## There are two families A and B. There are 4 men, 2 women and 1 child in family A

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November 1, 2022, 5:14 am

There are two families A and B. There are 4 men, 2 women and 1 child in family A and 2 men, 3 women and 2 children in family B. They recommended daily allowance for calories i.e. Men: 2000, Women: 1500, Children: 1200 and for proteins is Men: 50 gms., Women: 45 , Children: 30 gms. Represent the above information by matrices, using matrix multiplication calculate the total requirements of calories and proteins for each of the families.