Knowledge Quiz: Matrices

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Which of the following expressions will generate the following matrix?

\[ \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ \end{bmatrix} \]

matrix(1:6, 3, 2, byrow = TRUE)matrix(1:6, 3, 2)matrix(1:6, 2, 3, byrow = TRUE)matrix(1:6)matrix(6, 2, 3)

• Wrong. This command will return \[\begin{bmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \\ \end{bmatrix}\]
• Wrong. This command will return \[\begin{bmatrix} 1 & 4 \\ 2 & 5 \\ 3 & 6 \\ \end{bmatrix}\]
• Correct.
• Wrong. This command will return \[\begin{bmatrix} 1 \\ 2 \\ 3 \\ 4 \\ 5 \\ 6 \\ \end{bmatrix}\]
• Wrong. This command will return \[\begin{bmatrix} 6 & 6 & 6 \\ 6 & 6 & 6 \\ \end{bmatrix}\]

Which of the following expressions will convert matrix \(a\) into matrix \(b\)?

\[ \begin{align*} a &= \begin{bmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \\ \end{bmatrix} \\ b &= \begin{bmatrix} 1 & 2 \\ 3 & 5 \\ 4 & 6 \\ \end{bmatrix} \end{align*} \]

a[c(2, 3), c(1, 2)] <- matrix(3:6, 2, 2, byrow = TRUE)a[2, 3] <- c(4, 5)a[c(2, 3), c(1, 2)] <- matrix(3:6, 2, 2)a[c(2, 3), c(1, 2)] <- c(3, 4, 5, 6)a[c(2, 3), c(1, 2)] <- c(4, 5)

• Wrong. This command will produce \[\begin{bmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \\ \end{bmatrix}\]
• Wrong. This command will produce an error since we’re trying to overwrite columns that don’t exist.
• Correct.
• Correct.
• Wrong. This command will produce \[\begin{bmatrix} 1 & 2 \\ 4 & 4 \\ 5 & 5 \\ \end{bmatrix}\]