Math

QuestionFind the dimensions of the product matrix formed by multiplying any two of the following matrices: AA, BB, CC, DD.

Studdy Solution

STEP 1

Assumptions1. Matrix A is a3x1 matrix. Matrix B is ax matrix3. Matrix C is ax3 matrix4. Matrix D is ax1 matrix

STEP 2

The product of two matrices is defined only if the number of columns in the first matrix is equal to the number of rows in the second matrix.In mathematical terms, if we have two matrices and Q where is of dimension m x n and Q is of dimension p x q, then*Q is defined only if n = p. The resulting matrix will be of dimension m x q.

STEP 3

Let's consider all possible pairs of matrices and check if the product is defined for them.1. A and B The number of columns in A (1) is not equal to the number of rows in B (2). Therefore, A*B is not defined.
2. A and C The number of columns in A (1) is not equal to the number of rows in C (2). Therefore, A*C is not defined.
3. A and D The number of columns in A (1) is not equal to the number of rows in D (2). Therefore, A*D is not defined. . B and A The number of columns in B (2) is equal to the number of rows in A (3). Therefore, B*A is defined and the resulting matrix will be of dimension2 x1.
5. B and C The number of columns in B (2) is equal to the number of rows in C (2). Therefore, B*C is defined and the resulting matrix will be of dimension2 x3.
6. B and D The number of columns in B (2) is equal to the number of rows in D (2). Therefore, B*D is defined and the resulting matrix will be of dimension2 x1.
7. C and A The number of columns in C (3) is not equal to the number of rows in A (3). Therefore, C*A is not defined.
8. C and B The number of columns in C (3) is not equal to the number of rows in B (2). Therefore, C*B is not defined.
9. C and D The number of columns in C (3) is not equal to the number of rows in D (2). Therefore, C*D is not defined.
10. D and A The number of columns in D (1) is equal to the number of rows in A (3). Therefore, D*A is defined and the resulting matrix will be of dimension2 x1.
11. D and B The number of columns in D (1) is not equal to the number of rows in B (2). Therefore, D*B is not defined.
12. D and C The number of columns in D (1) is not equal to the number of rows in C (2). Therefore, D*C is not defined.

STEP 4

From the above analysis, we can conclude that the product of two matrices is defined for the following pairs B and A, B and C, B and D, and D and A. The dimensions of the resulting matrices are2x1,2x3,2x1, and2x1 respectively.

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