DATA 605_Week1_Discussion Questions

---

C10 (LA, chapter M, pg 172)

Perform the following calculations on the matrices and scalars below:

\[\mathbf{A} = \left[\begin{array} {rrr} 1 & 4 & -3 \\ 6 & 3 & 0 \end{array}\right] \]

\[\mathbf{B} = \left[\begin{array} {rrr} 3 & 2 & 1 \\ -2 & 6 & 5 \end{array}\right] \]

\[\mathbf{C} = \left[\begin{array} {rrr} 2 & 4 \\ 4 & 0 \\ -2 & 2 \end{array}\right] \]

\[\alpha = 4\]

\[\beta = \frac{1}{2}\]

# Create matrices and set scalars
A <- matrix(c(1, 4, -3, 6, 3, 0), nrow = 2, ncol = 3, byrow = TRUE)
B <- matrix(c(3, 2, 1, -2, 6, 5), nrow = 2, ncol = 3, byrow = TRUE)
C <- matrix(c(2, 4, 4, 0, -2, 2), nrow = 3, ncol = 2, byrow = TRUE)
alpha = 4
beta = .5

1. \(A + B\)

A + B

##      [,1] [,2] [,3]
## [1,]    4    6   -2
## [2,]    4    9    5

2. \(A + C\)

A + C

## Error in A + C: non-conformable arrays

The matrices cannot be summed as their dimension are different.

3. \(B^{t} + C\)

t(B) + C

##      [,1] [,2]
## [1,]    5    2
## [2,]    6    6
## [3,]   -1    7

4. \(A + B^{t}\)

A + t(B)

## Error in A + t(B): non-conformable arrays

The matrices cannot be summed as their dimension are different.

5. \(\beta\)\(C\)

beta * C

##      [,1] [,2]
## [1,]    1    2
## [2,]    2    0
## [3,]   -1    1

6. \(4A - 3B\)

4 * A - 3 * B

##      [,1] [,2] [,3]
## [1,]   -5   10  -15
## [2,]   30   -6  -15

7. \(A^{t} +\) \(\alpha\)\(C\)

t(A) + alpha * C

##      [,1] [,2]
## [1,]    9   22
## [2,]   20    3
## [3,]  -11    8

8. \(A + B - C^{t}\)

A + B - t(C)

##      [,1] [,2] [,3]
## [1,]    2    2    0
## [2,]    0    9    3

9. \(4A + 2B - 5C^{t}\)

4 * A + 2 * B - 5 * t(C)

##      [,1] [,2] [,3]
## [1,]    0    0    0
## [2,]    0   24    0