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In this lesson, we will learn how to use the properties of determinants to solve problems.

Q1:

Find the value of

Q2:

Find the value of | | | | − 5 2 − 4 0 5 0 3 0 0 | | | | .

Q3:

Using the properties of determinants, find the value of

Q4:

Use the properties of determinants to evaluate

Q5:

Without expanding, find the value of the determinant

Q6:

Q7:

Evaluate

Q8:

Q9:

Which of the following is equal to the determinant

Q10:

Consider the equation

Q11:

Determine all the possible values of 𝑥 given that 0 ≤ 𝑥 ≤ 3 6 0 ∘ ∘ .

Q12:

Use the properties of determinants to find the value of 𝑘 which makes 𝑥 a factor of the determinant

Q13:

Consider the equation Given that 𝑎 + 𝑏 + 𝑐 = − 1 , find its solution set.

Q14:

Find, without expanding, the value of the determinant

Q15:

Given that 𝑛 = | | | | 6 − 8 9 1 5 − 9 − 1 1 − 7 2 − 4 | | | | and 𝑚 = | | | | 1 8 − 2 4 2 7 9 0 − 5 4 − 6 6 − 3 5 1 0 − 2 0 | | | | , find a relation between 𝑚 and 𝑛 without expanding either determinant.

Q16:

Select the determinant that is equal to

Q17:

Find, in its simplest form, an expression for the determinant

Q18:

Select a factor of the determinant

Q19:

Q20:

Put the determinant | | | | − 4 − 5 7 8 − 4 1 6 5 2 2 3 8 | | | | in upper triangular form, and find its value.

Q21:

Which of the following pairs of points does the straight line represented by the equation pass through?

Q22:

Use the properties of determinants to find

Q23:

Consider

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