prepared by Abuzer Yakaryilmaz (QLatvia)

For the given vectors $ u = \myrvector{2 \\ -3 \\ 4 \\ 1} $ and $ v=\myrvector{-1 \\ 1 \\ -3 \\ 4} $, what is the second entry of $ 2u-3v $?


For the given vector $ u = \myrvector{-1 \\ 2 \\ -4} $, for which value of $r$ is the summation of the entries of vector $ r u $ is $ -6 $?


For the given vector $ u = \myrvector{-1 \\1 \\ -2} $, what is $ \norm{u} $?


For the given vector $ u = \myrvector{1 \\ -2 \\ 2 \\ 4} $, what is $ u \cdot u $?


For the given vectors $ u = \myrvector{1 \\ 2 \\ 3} $ and $ v = \myrvector{1 \\ 2 \\ -3} $, what is $ u \cdot v $?


Which of the following vector is perpendicular (orthogonal) to the vector $ \myrvector{-3 \\ 4} $?


For the given matrices $ M = \mymatrix{rrr}{1 & 0 & -2 \\ -2 & -1 & 3 \\ 0 & 1 & -2} $ and $ N = \mymatrix{rrr}{-1 & 3 & 2 \\ 0 & 2 & 1 \\ 4 & -1 & 0} $, what is the $ (2,3) $th entry of $ -2M + 3N $?


For the given matrices $ M = \mymatrix{rrr}{1 & 0 & -2 \\ -2 & -1 & 3 \\ 0 & 1 & -2} $ and $ N = \mymatrix{rrr}{-1 & 3 & 2 \\ 0 & 2 & 1 \\ 4 & -1 & 0} $, what is the $ (2,3) $th entry of $ N M $?


For the given matrices $ A = \mymatrix{rr}{1 & 0 \\ 2 & -1} $, what is $ A A^T $?


For the given matrices $ A = \mymatrix{rr}{1 & 0 \\ 2 & -1} $, what is $ A^T A $?


For the given vectors $ u = \myrvector{1 \\ 2} $ and $ v = \myrvector{1 \\ 3 \\ 5} $, what is the 4th entry of $ u \otimes v $?


For the given vectors $ u = \myrvector{1 \\ 2} $ and $ v = \myrvector{1 \\ 3 \\ 5} $, what is the 4th entry of $ v \otimes u $?


What is the $(3,4)$th entry of $ \mymatrix{rr}{1 & 0 \\ -1 & 2} \otimes \mymatrix{rr}{2 & 3 \\ 0 & 5} $?


What is the $(3,4)$th entry of $ \mymatrix{rr}{2 & 3 \\ 0 & 5} \otimes \mymatrix{rr}{1 & 0 \\ -1 & 2} $?


What is the $(3,3)$th entry of $ \mymatrix{rrr}{-1 & 2 & 0 \\ -2 & -1 & 2} \otimes \mymatrix{rr}{0 & -2 \\ 3 & -1 \\ -1 & 1 } $?


What is the $(5,5)$th entry of $ \mymatrix{rrr}{-1 & 2 & 0 \\ -2 & -1 & 2} \otimes \mymatrix{rr}{0 & -2 \\ 3 & -1 \\ -1 & 1 } $?