Asquare matrix a e rn is said to be skew-symmetric if a =-a prove that if a is skew-symmetric, then x'ax = 0 for all x e r". (hint the t t t quantity x'ax is scalar so that (x'ax) = x'ax)

You can use the given hint as follows:

Step-by-step explanation:

Let be a square matrix that is a skew-symmetric matrix. Since the matrix is matrix of size then it can be identified with an scalar. It is clear that . Then applying the properties of transposition we have

Then,

Then,

For all column vector of size .

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.