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15 problems match “systems of linear equations”. Clear

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11. Orthocentre of a triangle ●●○○○ 20 ptsFind the coordinates of the orthocentre of the triangle with vertices $A(5,6)$, $B(2,4)$ and $C(1,-3)$. Round each coordinate to two decimal places.
12. Two equations with percents ●●○○○ 20 ptsThe sum of $x$ and $y$ is 150. The sum of 5 percent of $x$ and 10 percent of $y$ is 11. Find $x$ and $y$.
13. Coordinates in a non-standard basis ●●○○○ 20 ptsLet $v = [6, 3, 2, 5]$, $a_1 = [2, 2, 2, 3]$, $a_2 = [1, 0, -1, 0]$ and $a_3 = [0, 1, 0, 1]$. Find the coordinates $[\alpha_1, \alpha_2, \alpha_3]$ of $v$ in terms of $a_1, a_2, a_3$, that is, the coefficients with $v = \alpha_1 a_1 + \alpha_2 a_2 + \alpha_3 a_3$.
14. Blue rectangles on a blackboard ●●●○○ 50 ptsBlue and red rectangles are drawn on a blackboard. Exactly 7 of the rectangles are squares. There are 3 more red rectangles than blue squares. There are 2 more red squares than blue rectangles. How many blue rectangles are there?
15. Sum of entries of inverse matrices ●●●○○ 50 ptsThe matrices $\begin{pmatrix} a & 1 & b \\ 2 & 2 & 3 \\ c & 5 & d \end{pmatrix}$ and $\begin{pmatrix} -5 & e & -11 \\ f & -13 & g \\ 2 & h & 4 \end{pmatrix}$ are inverses of each other. Find $a + b + c + d + e + f + g + h$.

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