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An employee receives a smaller merit increase than expected because their compa-ratio is already above 115%, even though they are one of the highest performers in the company. Do you think this compensation decision is appropriate? Why or why not? What challenges do organizations face when trying to balance?

BrightWave Consulting is reviewing its compensation system for Business Analysts. The salary range for this position is: Minimum: $48,000 Midpoint: $60,000 Maximum: $72,000 Three employees currently earn: Employee Current Salary Performance Rating Alex $54,000 Exceeds Expectations Brianna $60,000 Meets Expectations Carlos $70,000 Exceeds Expectations The company uses the following merit increase grid: Performance Rating Compa-Ratio 80–90% Compa-Ratio 91–110% Compa-Ratio 111–120% Exceeds Expectations 7% 5% 3% Meets Expectations 4% 3% 2% Below Expectations 2% 0% 0%  

Calculate each employee’s new salary after the merit increase. (Number only; 1000 or 1,000) Alex: $[AlexMoney] Brianna: $[BriannaMoney] Carlos: $[CarlosMoney]

Baby Yoda vs. Baby GrootThe Galactic Council has gathered to settle the most important debate in the universe:Who wins the Ultimate Cute-Off?Answer the following multiple-choice questions carefully. The fate of the galaxy depends on it. [You will get full points for whatever you choose]

Perform the indicated matrix operations.Note: Your answer will be in terms of the variables \(a\), \(b\), and \(c\).\(\begin{bmatrix} 1 & 2\\ a & -1\end{bmatrix}\begin{bmatrix} 3 & 0\\ 0 & 1\\ 2 & b\end{bmatrix}^T – 2\begin{bmatrix} 1 & 0 & c \\ 0 & 1 & 1\end{bmatrix}=\underline{\hspace{1in}}\)

Let B be the ordered basis for \(\mathbb{R}^3\) given by \(B=\left\{\begin{bmatrix} 1\\ -1\\ 0\end{bmatrix}, \begin{bmatrix} 0\\ 2\\ 1\end{bmatrix}, \begin{bmatrix} -1\\ 0\\ -2\end{bmatrix}\right\}\). Using this ordered basis, apply the Gram-Schmidt orthonormalization process to find a corresponding orthonormal basis for W.

Identify which one of the following sets of vectors in \(\mathbb{R}^3\) is linearly independent.

Let W be the subspace of \(\mathbb{R}^5\) spanned by \(B=\left\{\vec{v}_1, \vec{v}_2, \vec{v}_3\right\}=\left\{\begin{bmatrix} 1\\ 0\\ -1\\ 2\\ 3\end{bmatrix}, \begin{bmatrix} 4\\ 2\\ 0\\ -2\\ -5\end{bmatrix}, \begin{bmatrix} 0\\ 1\\ 2\\ 1\\ -1\end{bmatrix}\right\}\).Find a basis for \(W^{\perp}\), the orthogonal complement of W.

Identify which of the following vectors is orthogonal to \(\vec{u}=(2, 0, 3, 1)\).

An \(n\times n\) matrix \(A\) is diagonalizable if and only if…