Scalar and Matrix Multiplication

Question 1

What is the correct formula for the value of the determinant?

Revolt · Accepted Answer

ad - cb

Question 2

=

Revolt · Accepted Answer

72

Question 3

=

Revolt · Accepted Answer

7

Question 4

=

Revolt · Accepted Answer

-8

Question 5

What is the correct formula for calculating a 3 x 3 determinant?

Revolt · Accepted Answer

aei + bfg + cdh - gec - hfa - idb

Question 6

Calculate the value of the following determinants:=

Revolt · Accepted Answer

-25

Question 7

Which of the following statements are true?

Revolt · Accepted Answer

If any row of a square matrix is zero, its determinant is zero.; If all numbers in a matrix are equal, its determinant is zero.; The determinant of any zero matrix is zero.

Question 8

Use the determinant of the coefficient matrix to determine which of the following linear systems have unique solutions.

Revolt · Accepted Answer

mr001-1.jpg; mr001-2.jpg

Question 9

Consider the matrix:What is its determinant? Does the determinant depend on the variables? Make a conjecture.

Revolt · Accepted Answer

The determinant of the matrix is 8. This is calculated by multiplying the diagonal elements (1 * 2 * 4 = 8) because the matrix is upper triangular. The determinant does not depend on the variables x, y, and z. I conjecture that when all elements below the main diagonal are zero, the determinant is always the product of the main diagonal elements.

Question 10

=

Revolt · Accepted Answer

162

Scalar and Matrix Multiplication Answers

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