Question

Matrix: Did your matrix look like the one above? Check all that apply. My matrix is the same size. My matrix uses 0 to represent times to cities for which there was no flight. My matrix has the same values for each corresponding element.

Answer 1

The provided matrix represents the flight times between different cities. The rows represent the departing cities, and the columns represent the arriving cities. The elements of the matrix are the flight times in hours. Where there is no direct flight between two cities, a 0 is used to represent this in the matrix.

From the information provided:

- City 1 has flights to City 2, City 3, and City 5 with times 3.2, 3.5, and 5.4 hours, respectively.

- City 2 has flights to City 1, City 3, and City 4 with times 2.6, 1.8, and 2.1 hours, respectively.

- City 3 has a flight to City 4 with a time of 3.8 hours.

- City 4 has flights to City 1 and City 5 with times 6.8 and 7 hours, respectively.

- City 5 has a flight to City 4 with a time of 6.2 hours.

The correct checks for the matrix would be:

- [x] My matrix is the same size.

- [x] My matrix uses 0 to represent times to cities for which there was no flight.

- [x] My matrix has the same values for each corresponding element.

The provided matrix is correct based on the flight times given.

Answer 2

- Multiplies every element of a matrix by the same number: Scalar
- Requires two matrices that must be the same size: Neither
- Uses both multiplication and addition to find the result: Matrix
- Multiplies the row of one matrix by the column of another: Matrix

Scalar multiplication involves multiplying every element of a matrix by a constant (scalar) value. This operation preserves the matrix's structure but scales its values uniformly. For instance, if you have a matrix A and multiply it by the scalar k, each element in A will be multiplied by k.

Matrix multiplication, on the other hand, is a more intricate process. It requires two matrices, and the number of columns in the first matrix must match the number of rows in the second. The resulting matrix's dimensions will be the number of rows from the first matrix and the number of columns from the second. The individual elements of the resulting matrix are computed by taking the dot product of the corresponding row from the first matrix and column from the second matrix and summing these products.

Matrix multiplication involves both multiplication and addition, making it a more complex operation than scalar multiplication. It plays a crucial role in various mathematical and computational applications, such as solving systems of linear equations and transformations in linear algebra. The operation of multiplying the row of one matrix by the column of another facilitates these applications by combining the elements of the matrices in a systematic way.

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