Suppose a square matrix B is obtained by swapping rows $$s$$ and $$t$$ $$\left(s\ne t\right)$$ of another square matrix A. Which of the following are true?

a) $$\det\left(B\right)=-\det\left(A\right)$$

b) $$\det\left(B\right)=s\det\left(A\right)$$

c) $$\det\left(B\right)=\det\left(A\right)$$

d) $$t\det\left(B\right)=\det\left(A\right)$$

Suppose a square matrix B is obtained by multiplying row $$s$$ of another square matrix A by some non-zero scalar $$\mu$$ . Which of the following are true?

b) $$\det\left(B\right)=\mu\det\left(A\right)$$

a) $$\det\left(B\right)=-\det\left(A\right)$$

c) $$\det\left(B\right)=\det\left(A\right)$$

d) $$\mu\det\left(B\right)=\det\left(A\right)$$

Suppose $$U$$ is an $$n\times n$$ matrix in row echelon form. Which of the following can be used to calculate $$\det\ U$$ ?

d) $$\det\ U=u_{11}u_{22}...u_{nn}$$

a) $$\det\ U=u_{11}u_{12}...u_{1n}$$

b) $$\det\ U=u_{n1}u_{n2}...u_{nn}$$

c) $$\det\ U=u_{1n}u_{2n}...u_{nn}$$

Suppose $$A$$ is an $$n\times n$$ matrix such that $$\det\ A\ne0$$ . Which of the following are also true?

a) $$A$$ can be reduced to a matrix in REF which does not have a zero row.

d) Any system of linear equations whose LHS is represented by $$A$$ has a unique solution.

b) $$A$$ can be reduced to the zero matrix i.e. the $$n\times n$$ matrix whose every entry is 0.

Suppose $$A$$ is an invertible $$n\times n$$ . Which of the following are also true?

a) $$A$$ can be reduced to a matrix in REF which does not have a zero row.

d) Any system of linear equations whose LHS is represented by $$A$$ has a unique solution.

b) $$A$$ can be reduced to the zero matrix i.e. the $$n\times n$$ matrix whose every entry is 0.

0B2 Wk6 Tutorial MCQs (Determinants)

Quiz

•

Mathematics

•

University

•

Practice Problem

•

Hard

Nikesh Solanki

Used 24+ times

FREE Resource

9 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

What is the determinant of A?

-44

-36

28

44

2.

MULTIPLE CHOICE QUESTION

45 sec • 1 pt

Which of the formulae in the picture is the formula for calculating the determinant of a 3x3 matrix?

a

b

c

d

3.

MULTIPLE SELECT QUESTION

45 sec • 1 pt

a) Another name for the (i,j)-th entry of A.

b) The matrix obtained by deleting the i-th row and j-th column of A.

c) The matrix obtained by deleting the j-th row and i-th column of A.

d) The determinant of the matrix obtained by deleting the i-th row and j-th column of A.

4.

MULTIPLE CHOICE QUESTION

45 sec • 1 pt

5.

MULTIPLE CHOICE QUESTION

45 sec • 1 pt

6.

MULTIPLE SELECT QUESTION

1 min • 1 pt

7.

MULTIPLE SELECT QUESTION

1 min • 1 pt

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

11 questions

Untitled Quiz

Quiz

•

6th Grade - University

10 questions

Let's Play Together

Quiz

•

University - Professi...

13 questions

Juego integrador de Matemática!

Quiz

•

University

10 questions

Equation of the circle

Quiz

•

10th Grade - University

10 questions

MGSE.7.G2 (Triangles)

Quiz

•

KG - University

10 questions

ลำดับและอนุกรม (อนุกรม)-ONET

Quiz

•

10th Grade - University

12 questions

Baris dan Deret

Quiz

•

University

10 questions

Chapter1-intro to statistics part1

Quiz

•

University

Popular Resources on Wayground

15 questions

Fractions on a Number Line

Quiz

•

3rd Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

54 questions

Analyzing Line Graphs & Tables

Quiz

•

4th Grade

$fractions$

22 questions

fractions

Quiz

•

3rd Grade

20 questions

Main Idea and Details

Quiz

•

5th Grade

20 questions

Context Clues

Quiz

•

6th Grade

15 questions

Equivalent Fractions

Quiz

•

4th Grade

Discover more resources for Mathematics

20 questions

Ch. 7 Quadrilateral Quiz Review

Quiz

•

KG - University

7 questions

Introduction to Fractions

Interactive video

•

1st Grade - University

18 questions

Exam Review

Quiz

•

University

16 questions

Parallel, Perpendicular, and Intersecting Lines

Quiz

•

KG - Professional Dev...

25 questions

Math College Placement Practice #2

Quiz

•

11th Grade - University

10 questions

One Step Equations Multiply and Divide

Quiz

•

University