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WorksheetsEDMATH 300
Total questions: 30
Worksheet time: 25mins
A rectangular array of numbers, in which not only the value of the number is important but also its position in the array.
(a)
The numbers in the array are called (a) of the matrix.
The size of the matrix is described by the number of its (a) .
An m x n matrix is a matrix which has m rows
and n (a) .
The elements (or the entries) of a matrix are generally enclosed in brack-
ets, double-subscripting is used to index the elements. The First subscript
always denote the (a) position.
When m=n , the matrix is said to be a
(a)
The main diagonal in a square matrix contains the elements (a)
A matrix is said to be (a) if all its entries below the main
diagonal are 0.
A matrix is said to be (a) if all its entries above the main
diagonal are 0.
If all the entries of a square matrix are zero, except those entries on the
main diagonal, then we say the matrix is a (a) .
An n x n matrix having ones on the main
diagonal, and zeroes everywhere else. It is usually denoted In .
(a)
We say that two matrices are equal whenever they have the same (a) , and their corresponding entries are equal.
A (a) is a vector which has only one row. In other words, it is an
1 x n matrix.
A (a) is a vector which has only one column. In other words,
it is an m x 1 matrix.
What is the size or dimension of the matrix?
3 x 2
2 x 3
m x n
3 columns by 2 rows
Which of the following best describe the given matrix?
3 x 2 matrix
square (3 x 3) matrix
square (3 x 2) matrix
identity matrix
Choose answers that describes the given matrix.
3 x 3 matrix
identity matrix
square matrix
3 x 3 upper and lower triangular matrix
Choose answers that best describes the given matrix.
4 x 4 matrix
4 x 4 upper triangular matrix
4 x 4 lower triangular matrix
diagonal matrix
Choose answers that best describes the given matrix.
column vector
row vector
4 x 1 matrix
1 x 4 matrix
Choose answers that best describes the given matrix.
row vector
1 x 3 matrix
3 x 1 matrix
column vector
Only matrices having the same size can be added or subtracted.
True
False
Choose answers that completes the sentence. To add (subtract) two matrices having the same size,
simply add (sub-
tract) the corresponding entries.
In other words, if C = A + B, then
cij = aij + bij
simply add (sub-
tract) the entries.
In other words, if C = A + B, then
aij = bij + cij
Subtract the given matrices. Choose the correct answers.
Can not be done. The matrices do not have the
same dimension
Only matrices having the same size can be added or subtracted.
The result is a matrix of the same size.
The figure shows multiplication of matrices. 4 is a 1 x 1 matrix also called (a) .
What will be the result when we multiply a row vector by a column vector? Use the given figure.
1 x 1 matrix
scalar
100
This cannot be done , the vectors have the same
number of elements.
Let us assume that A is m x p and B is q x n. The product of A and B, denoted AB can be performed only if p = q.
In other words, the number of columns of the first matrix, A must be the
same as the number of rows of the second matrix, B.
True
False
What can we infer from the given figure/illustration?
matrix multiplication will not be commutative
matrix multiplication will always be commutative
multiplying two 3 x 3 matrices will result to a 3 x 3 matrix
What is the answer?
identity matrix
upper triangular matrix
upper and lower triangular matrix
square matrix
If A is an m x n matrix, then the
transpose of A, denoted AT is the n x m matrix obtained from A by interchanging the rows and columns of A.
True
False
The following statements are correct EXCEPT
If A is a square matrix (n x n) then the
trace of A, denoted tr (A), is defined to be the sum of its entries on the main
diagonal of A.
tr (A) is not defined if A is not a square matrix.
If A is a square matrix (n x n) then the
trace of A, denoted tr (A), is defined to be the product of its entries opposite on the main
diagonal of A.
