Suppose M is a 3 \times 2 matrix.
How many rows does M have?
How many columns does M have?
State whether the following matrices are valid:
State how many elements there are in the following:
A matrix with 4 rows and 5 columns.
The third column of a 7 \times 8 matrix.
The leading diagonal of a 4 \times 4 matrix.
A square matrix with 5 rows.
State the dimensions of the following matrices in the form m \times n:
State the entry at a_{23} \text{ in } A = \begin{bmatrix} -2 & -5 & 5 \\ -1 & 1 & -7 \\ 8 & 4 & 7\end{bmatrix}.
State the location of 5 in the form a_{ij} for the matrix A=\begin{bmatrix} -3 & 5 & -4 \\ 3 & -5 & 1 \\ -6 & -1 & 6 \end{bmatrix}.
Consider A=\begin{bmatrix} -5 & -8 & 9 \\ -6 & 2 & 8 \end{bmatrix} and B= \begin{bmatrix} 7 & -9 \\ 3 & 6 \\ -2 & 4 \end{bmatrix}. Find:
a_{21} - b_{11}
a_{13} \times b_{31}
M is a 3 \times 3 matrix. The elements of M are determined by the rule m_{ij}=i + j. Write down the matrix M.
A is a 3 \times 2 matrix. The elements of A are determined by the rule a_{ij} = i + 2 j - 2. Write down the matrix A.
B is a 4 \times 4 matrix. The elements of B are determined by the rule b_{ij} = i^2 . Write down the matrix B.
C is a 3 \times 3 matrix. The elements of C are determined by the rule c_{ij} = 10i + j. Write down the matrix C.
A matrix with three less rows than columns has 54 elements. Find the dimensions of this matrix.
If a matrix has 10 elements, list the different dimensions it could possibly have.
If a matrix has 24 elements, how many different dimensions could it possibly have?
Define:
A matrix
A square matrix
A row matrix
An identity matrix
If a column matrix contains 6 elements, state the number of rows the matrix has.
State the number of columns the identity matrix I_4 contains.
Which of the following matrices is a square matrix?
Which of the following matrices is a zero matrix?
Construct the following:
A row matrix consisting of the numbers -4, 1 \text{ and } 4.
A column matrix consisting of the numbers 5, -2, 2 \text{ and } 4.
A 2 \times 2 identity matrix.
A 3 \times 3 zero matrix.
A 3 \times 3 diagonal matrix with the numbers 5, 6 \text{ and } 1 on the leading diagonal.