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HSA.REI.C.8 Tutor Intake — Matrix Equations

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Grade 9·8 problems·~13 min·Common Core Math - HS Algebra·standard·hsa-rei-c-8
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A

Concepts

1.

For matrix multiplication ABAB, which condition must be met?

2.

Is matrix multiplication commutative? That is, does AB=BAAB = BA always hold?

3.

Consider the system:
3x+0⋅y=93x + 0 \cdot y = 9
2x+5y=72x + 5y = 7

Which matrix AA correctly represents the coefficient matrix?

B

Procedures

1.

Write the matrix equation Ax=bAx = b for the system:
2x+3y=82x + 3y = 8
x−y=1x - y = 1

A = \begin{bmatrix}   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   &   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   $\  ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   &  ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   \end{bmatrix},, x = \begin{bmatrix}x\y\end{bmatrix},, b = \begin{bmatrix}   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   \\  ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   \end{bmatrix}$

a11:
a12:
a21:
a22:
b1:
b2:
2.

Compute AxAx where A=[231−1]A = \begin{bmatrix}2 & 3\\1 & -1\end{bmatrix} and
x=[21]x = \begin{bmatrix}2\\1\end{bmatrix}.

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