If A and B are 4 * 6 matrices and C is a 7 * 4 matrix, which of the following are defined? 1. CA.2. B^T * C^T.3. AC.4. A-B.5. B-C.6. B^T.

1. CA is defined

2. B^T * C^T defined

3. AC is NOT defined

4. A - B is defined

5. B - C is NOT defined

6. B^T is defined

Hence, 1,2,4, and 6 are defined

Step-by-step explanation:

Order of the matrices:

Matrix A is a (4 × 6) matrix  

Matrix B is a (4 × 6) matrix

Matrix C is a (7 × 4) matrix

To determine which are defined

1. CA

CA means product of Matrix C and Matrix A

To determine the product of two matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix. For example, given that matrix X is a (m × n) matrix, matrix Y is a (n × k) matrix and matrix Z is (k × n) matrix. From the definition above,

XY can be determined because number of columns in X equals number of rows in Y

XZ cannot be determine  because number of columns in X is not equal to the number of rows in Z.

YZ can be determined because number of columns in Y equals number of rows in Z

(NOTE: A matrix of order (m × n) means the matrix has m rows and n columns)

Hence, for CA

Matrix C is a (7 × 4) matrix

Matrix A is a (4 × 6) matrix

Number of columns in C equals number of rows in A, hence CA is defined

2. B^T * C^T

B^T means transpose of matrix B

Transpose of a matrix is defined as a new matrix whose rows are the same as the columns of the original matrix and whose columns are the rows of the original matrix. Hence, for a matrix of order (m × k), the transpose of the matrix will have an order (k × m).

Hence,

Matrix B is a (4 × 6) matrix

∴B^T gives a matrix of order (6 × 4)

Matrix C is a (7 × 4) matrix

∴ C^T gives a matrix of order (4 × 7)

Since the number of columns in B^T equals the number of rows in C^T, then  B^T * C^T defined

3. AC

Matrix A is a (4 × 6) matrix

Matrix C is a (7 × 4) matrix

The number of columns in A is NOT equal to the number of rows in C, hence AC is NOT defined

4. A - B

To find the difference between two matrices, the matrices must have the same order.

Matrix A is a (4 × 6) matrix  

Matrix B is a (4 × 6) matrix

Since matrices A and B have the same order [(4 × 6)], hence A - B is defined

5. B - C

Matrix B is a (4 × 6) matrix

Matrix C is a (7 × 4) matrix

Since matrices B and C are of different orders [(4 × 6) and (7 × 4) respectively], then B - C is NOT defined

6. B^T

B^T means the transpose of matrix B

Matrix B is a (4 × 6) matrix

From the above definition

B^T gives a (6 × 4) matrix

Hence, B^T is defined

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to

then mult. both sides by 75 we get the ratio

75 mi. to

simplifying we get

75 mi. to

or 1.25 hr.

step-by-step explanation:

i found the life tables for the year 2012. 

life table of males at age 30. probability of dying between ages x and x+1

total population:  

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:  

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old. 

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

                                          probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497