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Review set

Matrix-vector products and the column reading

The questions ask you to move between the row and column readings of a product and to choose whichever answers the question posed. Computing A x comes back quickly; reaching for the column reading when the question is about what is possible is what needs practice.

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2 questions, chosen for youHints availableNo time limit

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What this covers

  • Compute a matrix-vector product

    Given a matrix and a vector, the learner can compute A x and decide whether a product is defined before forming it.

  • Read a matrix product as an action on columns

    Given A x , the learner can express it as a linear combination of the columns of A weighted by the entries of x , and use that reading to decide questions about which vectors A x can reach.

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