Question

Identify matrix A as a square matrix, column matrix, row matrix, or neither. Also, determine the size of A. Provide the negative (additive inverse) of matrix A.

a) Square matrix, size 3x3, negative of A
b) Row matrix, size 2x4, negative of A
c) Column matrix, size 4x2, negative of A
d) Neither square, column, nor row matrix

Answer 1

Matrix A can be identified as a square, row, or column matrix based on its properties and size. The negative of matrix A is obtained by changing the sign of each element in A.

Step-by-step explanation:

a) Matrix A is a square matrix because it has the same number of rows and columns. The size of A is 3x3.

The negative (additive inverse) of matrix A is obtained by changing the sign of each element in A. For example, if A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]], then the negative of A is [[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]].

b) Matrix A is a row matrix because it has only one row. The size of A is 2x4.

The negative of matrix A is obtained by changing the sign of each element in A. For example, if A = [1, 2, 3, 4], then the negative of A is [-1, -2, -3, -4].

c) Matrix A is a column matrix because it has only one column. The size of A is 4x2.

The negative of matrix A is obtained by changing the sign of each element in A. For example, if A = [[1], [2], [3], [4]], then the negative of A is [[-1], [-2], [-3], [-4]].

d) Matrix A is neither a square matrix, nor a column matrix, nor a row matrix.