What is the difference between a direction cosines matrix and a rotation matrix? O A direction cosines matrix can do only rotations around one coordinate axis at a time, either around x-, y- or z-axis. While a rotation matrix can do any rotation. O A rotation matrix can do only rotations around one coordinate axis at a time, either around x-, y- or z- axis. While a direction cosines matrix can do any rotation. O A rotation matrix is the same thing as a direction cosines matrix O A rotation matrix can only be 3x3, while a direction cosines matrix can be either 2x2 or 3x3.

What geometric transformation of 3D space happens in this matrix-vector multiplication? 010 -1 0 0 0 01 9).( (3) Please note: All rotation directions to be understood as when looking along the rotation axis towards the origin. O Clockwise rotation by 90 degrees around the x3 axis Counter-clockwise rotation by 90 degrees around the x3 axis Clockwise rotation by 90 degrees around the x₂ axis Counter-clockwise rotation by 90 degrees around the x2 axis O Clockwise rotation by 90 degrees around the x₁ axis Counter-clockwise rotation by 90 degrees around the x₁ axis O Mirroring across the x₁-x2 plane Mirroring across the x₁-x3 plane Mirroring across the X₂-X3 plane

Determine whether or not the following sets S of 2 x 2 matrices are linearly independent. 4 {(5).(-26 -20)} -4 Select an Answer Select an Answer Select an Answer Select an Answer V V 1. S= 2. S= 3. S= 4 -16 -40 {(35).(-* *}} -4 4. S= -16 {(5).(-4) 17 -31 (8) (-₂4) (73)} 9 10 -20 2 = {(21)-(32) (43)}

Hello. Please answer the attached Linear Algebra question correctly and completely. Please show all of your work.  *If you answer the question correctly and show all of your work, I will give you a thumbs up. Thanks.