lab 2 · matrices (R) — source
A. Stamm 
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# ============================================================
# Lab 2: Matrices: build, algebra, and column-wise work
# The R Statistical Language · Session 3
#
# Work through the exercises. Comment your thought process
# as you go: a reproducible script is one a stranger can read.
# ============================================================
## Part A: build & inspect ---------------------------------
# A1. Build M <- matrix(1:20, nrow = 4, ncol = 5).
# Report dim(M), nrow(M), ncol(M), rowSums(M), colMeans(M).
# A2. Confirm the fill is column-major: print M and check where
# the 1 and the 6 land. Rebuild with byrow = TRUE and compare.
# A3. Add a 6th column with cbind(M, c(100, 200, 300, 400)).
# Bind two extra rows with rbind(M, c(1, 2, 3, 4, 5)).
## Part B: arithmetic & recycling --------------------------
# B1. Compute M * 2 and M + c(10, 20, 30, 40) (a length-4 vector).
# Which axis did the vector recycle along?
# B2. Column-scale M: M * matrix(c(1, 10, 100, 1000, 10000), 1, 5).
# What does each column get multiplied by?
## Part C: linear algebra ----------------------------------
# C1. A <- matrix(c(4, 2, 1, 3), nrow = 2). Compute:
# A %*% A, t(A), det(A), solve(A). Verify A %*% solve(A)
# is (nearly) the identity.
# C2. Build a 4x4 diagonal matrix with diag(4), then diag(c(2, 3, 5, 7)).
# What does diag(M) return for a rectangular matrix M?
## Part D: row/column summaries & apply --------------------
# D1. Using M from Part A, compute apply(M, 1, max) and apply(M, 2, max).
# Which MARGIN is which?
# D2. range of each column: apply(M, 2, function(x) max(x) - min(x)).
## Part E: standardise (bridge to functions) ---------------
# E1. Z-score every column of M: subtract the column mean, then
# divide by the column sd. Use colMeans(M), apply(M, 2, sd),
# and two sweep() calls (or scale(M) to check yourself).
# Confirm the result: colMeans ~ 0, apply(., 2, sd) ~ 1.