Unit 5 - Matrices and Vectors

Question 1

A matrix with just one column is also called

Answer 1

a vector

Question 2

An m × n matrix is a

Answer 2

rectangular array of values (called entries), arranged in m rows and n columns s (where m and n are positive integers)

Question 3

If M is a matrix, then its transpose is a

Answer 3

a matrix that is the “flipped” version of M, where each row of M becomes a column, and each column of M becomes a row.

Question 4

Consider the following 2 × 3 matrix:
M =
[10 20 30]
[40 50 60]

the transpose of M is the following

Answer 4

3 × 2 matrix:
M=
[10 40]
[20 50]
[30 60]

Question 5

The scalar multiplication is the product between a real number c and a matrix M; the result is

Answer 5

a matrix with the values in M multiplied by c.

Question 6

Consider the following 2 × 3 matrix:
M =
[10 20 30]
[40 50 60]

then scalar multiplication 2M is the following

Answer 6

=
[20 40 60 ]
[80 100 120]

Question 7

The addition between two matrices M and N is only defined if

Answer 7

M and N have the same number of rows and columns

Question 8

Consider the following 2 × 3 matrices:
M =
[10 20 30]
[40 50 60]

N =
[0.1 0.2 0.3]
[0.4 0.5 0.6]

M + N =

Answer 8

M + N =
[10.1 20.2 30.3]
[40.4 50.5 60.6]

Question 9

Since M is a 3 × 2 matrix, and N is a 2 × 4 matrix, we know that the product MN is going to be a

Answer 9

3 × 4 matrix

Question 10

Matrix multiplication requires

Answer 10

the number of rows of one to match the number of columns of the other

Question 11

During matrix multiplication to compute an entry at row i and column j you

Answer 11

multiply each value in row i
of M to the corresponding value on column j of N, and sum the results.