Question

$Let space straight A space equals space open square brackets table row cell cos space straight theta end cell cell sin space straight theta end cell row cell negative sin space straight theta end cell cell cos space straight theta end cell end table close square brackets comma space show space that space straight A squared equals open square brackets table row cell cos space 2 straight theta end cell cell space sin space 2 straight theta end cell row cell negative sin space 2 straight theta end cell cell cos space 2 straight theta end cell end table close square brackets$

Solution

Here space straight A space equals bold Let bold space bold A bold space bold equals bold space open square brackets table row cell bold cos bold space bold theta end cell cell bold sin bold space bold theta end cell row cell bold minus bold sin bold space bold theta end cell cell bold cos bold space bold theta end cell end table close square brackets bold therefore bold space bold space bold A to the power of bold 2 bold space bold equals bold A bold space bold. bold space bold A bold space bold equals bold space bold Let bold space bold A bold space bold equals bold space open square brackets table row cell bold cos bold space bold theta end cell cell bold sin bold space bold theta end cell row cell bold minus bold sin bold space bold theta end cell cell bold cos bold space bold theta end cell end table close square brackets bold. open square brackets table row cell bold cos bold space bold theta end cell cell bold sin bold space bold theta end cell row cell bold minus bold sin bold space bold theta end cell cell bold cos bold space bold theta end cell end table close square brackets bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold equals bold space open square brackets table row cell bold cos to the power of bold 2 bold space bold theta end cell cell bold minus bold sin to the power of bold 2 bold space bold theta end cell row cell bold minus bold sin bold space bold theta bold space bold cos bold space bold theta end cell cell bold cos to the power of bold 2 bold space bold theta bold space bold minus bold space bold sin to the power of bold 2 bold space bold theta end cell end table close square brackets bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold equals bold space open square brackets table row cell bold cos bold space bold 2 bold theta end cell cell bold sin bold space bold 2 bold theta end cell row cell bold minus bold sin bold space bold 2 bold theta end cell cell bold cos bold space bold 2 bold theta end cell end table close square brackets

For Daily Free Study Material Join wiredfaculty

Matrices

Some More Questions From Matrices Chapter

If a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements?

If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?

If a matrix A has 12 elements, what arc the possible orders it can have 7 What if it has 7 elements ?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction