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IntermediateLinear Algebra10 min

Rank in disguise

A=(123246369)A = \begin{pmatrix} 1 & 2 & 3 \\ 2 & 4 & 6 \\ 3 & 6 & 9 \end{pmatrix}

State the rank of A, then describe its null space and column space.

RankNull spaceRank–nullity theorem
Quick investigations

Sixty seconds. One decision.

Spot the mistakeFoundationHigh School60s

A student solves x² = 5x and concludes x = 5. What went wrong?

x2=5x  ⇒  x=5x^2 = 5x \;\Rightarrow\; x = 5

Topic: Quadratic equations

Estimate firstFoundationMiddle School30s

Without a calculator, is √72 closer to 8 or to 9?

Topic: Number sense

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