Suppose that
\begin{pmatrix} -107 \ -347 \ 939 \ -359 \ -51 \ 180 \end{pmatrix} u_1 = \begin{pmatrix} -32 \ 575 \ -18 \ -920 \ 919 \ -758 \end{pmatrix} , u_3 = \begin{pmatrix} 227 \ 820 \ 28 \ -460 \ -836 \ 128 \end{pmatrix} , and \ u_4 = \begin{pmatrix} 247 \ -765 \ 523 \ 39 \ 456 \ 879 \end{pmatrix}
To avoid typing errors, you can copy and past the following sequences to your Maple worksheet to form entries of
the vectors.
-107, -347, 939, -359, -51, 180
-32, 575, -18, -920, 919, -758
227, 820, 28, -460, -836, 128
247, -765, 523, 39, 456, 879
(a) Find the dot product of $u_1$ and $u_2$. Enter your answer in the box below.
$u_1 \cdot u_2 = $ Number
(b) Suppose that A is the matrix whose columns are these four vectors in order, i.e.
$A = (u_1 \mid u_2 \mid u_3 \mid u_4)$
\begin{pmatrix} -26 \ -71 \ 52 \ 29 \end{pmatrix}
Let $v$ be the vector
Hence $Av$ is a linear combination of the form
$\lambda_1 u_1 + \lambda_2 u_2 + \lambda_3 u_3 + \lambda_4 u_4$
Enter the values of $\lambda_1, \lambda_2, \lambda_3, \lambda_4$ in the boxes below
$\lambda_1 = $ Number $\lambda_2 = $ Number $\lambda_3 = $ Number $\lambda_4 = $ Number
(c) Suppose that $Av = \begin{pmatrix} b_1 \ b_2 \ \vdots \ b_6 \end{pmatrix}^T$
Enter the value of $b_1$ in the box below
$b_1 = $ Number
