A 3 × 3 matrix A = [aᵢⱼ] has aᵢⱼ = 0 when i ≠ j and aᵢⱼ = 4 when i = j. What is A?

Question 23

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A 3 × 3 matrix $A = [a_{ij}]$ has $a_{ij} = 0$ when $i \ne j$ and $a_{ij} = 4$ when $i = j$ . What is $A$ ?

An identity matrixCorrect answerYour answerA zero matrixCorrect answerYour answerA scalar matrixCorrect answerYour answerA diagonal matrix that is not scalarCorrect answerYour answer

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CorrectNot quiteAnswer C

Correct answer: C

Every element off the leading diagonal is 0, so $A$ is diagonal.
Its diagonal elements are all 4, equal but not 1, so it is a scalar matrix and not the identity.

Concept: Scalar matrices
Typical timeTypical: 90 s
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A 3 × 3 matrix A=[aij]A = [a_{ij}]A=[aij​] has aij=0a_{ij} = 0aij​=0 when i≠ji \ne ji=j and aij=4a_{ij} = 4aij​=4 when i=ji = ji=j. What is AAA?

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A 3 × 3 matrix $A = [a_{ij}]$ has $a_{ij} = 0$ when $i \ne j$ and $a_{ij} = 4$ when $i = j$ . What is $A$ ?