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Matrices · Question 9 of 106

Question 9

MediumOriginal question

A=[aij]A = [a_{ij}] is a 2 × 2 matrix with aij=i2−ja_{ij} = i^2 - j. Which matrix is AA?

Options for question 9

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. Row 1 (i=1i = 1): 1−1=01 - 1 = 0 and 1−2=−11 - 2 = -1.

  2. Row 2 (i=2i = 2): 4−1=34 - 1 = 3 and 4−2=24 - 2 = 2.

  3. So A=[0−132]A = \begin{bmatrix}0 & -1 \\ 3 & 2\end{bmatrix}.

Worth noting

[03−12]\begin{bmatrix}0 & 3 \\ -1 & 2\end{bmatrix} is the transpose of AA: ii was taken as the column.

Concept
Constructing a matrix from a rule for its elements
Typical time
90 s
Your time
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The rule this testsA matrix, its elements and order
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Ten questions from Matrices, at your own pace.

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Ten questions from Matrices, at your own pace.