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In this lesson, we will learn how to differentiate between invertible and singular matrices.

Q1:

Is the following matrix invertible?

Q2:

Under what condition on is the following matrix invertible?

Q3:

Is there any value of for which the matrix has no inverse?

Q4:

Q5:

Q6:

Which of the following matrices is singular?

Q7:

Under what condition on π and π is the following matrix invertible?

Q8:

Find the value of π₯ that makes the matrix οΌ π₯ β 8 β 5 β 1 ο singular.

Q9:

Find all the values of π₯ for which the matrix οΌ π₯ β 1 1 5 1 5 π₯ + 1 1 ο is singular.

Q10:

Find the value of π₯ that makes the matrix singular.

Q11:

Find all the values of π₯ , where 0 β€ π₯ < 3 6 0 β β , which make the following matrix singular:

Q12:

Find the set of real values of π for which has a multiplicative inverse.

Q13:

For the matrix does there exist a value of for which it fails to have an inverse? if so, what is this value?

Q14:

Find the set of real values of π₯ for which οΌ β 4 π₯ 6 8 β 1 7 π₯ ο has no multiplicative inverse.

Q15:

Find the set of real values of π for which οΌ π 8 8 π ο has no multiplicative inverse.

Q16:

Find the set of real values of π for which the following matrix has a multiplicative inverse

Q17:

Find the set of real values of π for which ο½ π π β π 1 ο 2 has a multiplicative inverse, where π = β 1 2 .

Q18:

Does the matrix have a multiplicative inverse?

Q19:

Find the set of real values of ( π₯ ) that make the following matrix singular.

Q20:

Find the set of real values of π₯ that make the matrix singular.

Q21:

Suppose π΄ is matrix in β ο© Γ ο© and v is a vector in β ο© and consider this statement: there exists a solution x to the equation π΄ = x v . Which of the following is true?

Q22:

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