Invertiable for all values of theta

[salistoun]

Hi all,

How do you go about solving this question as it says:

Show that the matrix:

| costheta sintheta 0 |
B= | -sintheta costheta 0 |
| 0 0 1 |

is invertible for all values of theta [Hint. Show that det(B) is not equal of all values of theta ]

Thanks

Stephen

 

[tiny-tim]

Hi Stephen!

Show that the matrix:

| costheta sintheta 0 |
B= | -sintheta costheta 0 |
| 0 0 1 |

is invertible for all values of theta [Hint. Show that det(B) is not equal of all values of theta

I don't get it …

everybody knows that the inverse of that is the same but with -θ instead of θ;

and det(B) is always 1.

 

[HallsofIvy]

You are given a hint. Did it not occur to you to do what the hint said? What is the determinant of that matrix?

 

[pwsnafu]

[Hint. Show that det(B) is not equal of all values of theta ]

Is that a typo?