MATRICES ASSIGNMENT

Given the matrices:

$a) [\begin{matrix} - 1 & 1 & 0 & 3 \\ 4 & - 3 & - 7 & - 9 \end{matrix}] b) [\begin{matrix} - 6 & 2 & 0 \\ 3 & - 3 & 4 \\ - 5 & - 11 & 9 \end{matrix}] c) [\begin{matrix} 1 & - 2 & 5 & - 2 \end{matrix}] d) [\begin{matrix} - 2 & 0 \\ 0 & - 3 \end{matrix}] e) [\begin{matrix} 3 \end{matrix}]$
a) What is the dimension of each matrix?
b) Which matrices are square?
c) Which matrices are symmetric?
d) Which matrix has the entry at row 3 and column 2 equal to -11?
e) Which matrices has the entry at row 1 and column 3 equal to 10?
f) Which are column matrices?
g) Which are row matrices?
h) Find $A^{T}, C^{T}, E^{T}, G^{T}$ .

For each matrix below, determine the order and state whether it is a square matrix.

$A = [\begin{matrix} - 1 & 23 & 10 \\ 0 & - 2 & - 11 \end{matrix}], B = [\begin{matrix} - 6 & 2 & 10 \\ 3 & - 3 & 4 \\ - 5 & - 11 & 9 \\ 1 & - 1 & 9 \end{matrix}], C = [\begin{matrix} - 3 & 2 & 9 & - 5 & 7 \end{matrix}] D = [\begin{matrix} - 2 & 6 \\ - 5 & 2 \end{matrix}], E = [\begin{matrix} 3 \end{matrix}], F = [\begin{matrix} 3 \\ 5 \\ - 11 \\ 7 \end{matrix}], G = [\begin{matrix} - 6 & - 4 & 23 \\ - 4 & - 3 & 4 \\ 23 & 4 & 9 \end{matrix}]$

a) order: 2 × 4. Number of rows and columns are not equal therefore not a square matrix.
b) order: 3 × 3. Number of rows and columns are equal therefore this matrix is a square matrix.
c) order: 1 × 4. Number of rows and columns are not equal therefore not a square matrix. A matrix with one row is called a row matrix (or a row vector).
d) order: 2 × 2. Number of rows and columns are equal therefore this is square matrix.
e) order: 1 × 1. Number of rows and columns are equal therefore this matrix is a square matrix.

Questions on Matrices: Part B

1) Given the matrices:

a) Which of the above matrices are diagonal?
b) Which of the above matrices are lower triangular?
c) Which of the above matrices are upper triangular?

Solutions to the Questions in Part A

a) A: 2 × 3, B: 4 × 3, C: 1 × 5, D: 2 × 2, E: 1 × 1, F: 4 × 1, G: 3 × 3,
b) D, E and G
c) E and G
d) B
e) A and B
f) E and F
g) E and C
h)

Solutions to the Questions in Part B

a) C and E
b) B
c) A and D

TUMUHEIRE AGNES

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MATRICES ASSIGNMENT

Questions on Matrices: Part B

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Solutions to the Questions in Part B

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