Question

Let A be a \( 3 \times 3 \) matrix. Choose correct statements: (i) \( \operatorname{det}(-A)=\cdot \operatorname{det}(A) \) (ii) It A has two equal rows, then \( \operatorname{det}(\mathrm{A})=0 \) (iii) If \( \operatorname{det}(A)=0 \), then \( A \) has two equal rows. A. All of (i), (ii) and (iii) B. (ii) and (iii) C. (i) and (ii) D. (iii) E (i) and (iii)

          Let A be a \( 3 \times 3 \) matrix. Choose correct statements:
(i) \( \operatorname{det}(-A)=\cdot \operatorname{det}(A) \)
(ii) It A has two equal rows, then \( \operatorname{det}(\mathrm{A})=0 \)
(iii) If \( \operatorname{det}(A)=0 \), then \( A \) has two equal rows.
A. All of (i), (ii) and (iii)
B. (ii) and (iii)
C. (i) and (ii)
D. (iii)

E (i) and (iii)

Let A be a 3 × 3 matrix. Choose correct statements:
(i) det(-A)=·det(A)
(ii) It A has two equal rows, then det(A)=0
(iii) If det(A)=0, then A has two equal rows.
A. All of (i), (ii) and (iii)
B. (ii) and (iii)
C. (i) and (ii)
D. (iii)

E (i) and (iii)

Added by William J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ahmet Yavas

Step 1

Therefore: \[ \operatorname{det}(-A) = (-1)^3 \operatorname{det}(A) = -\operatorname{det}(A) \] So, statement (i) is correct. Show more…

Show all steps

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Let A be a \( 3 \times 3 \) matrix. Choose correct statements: (i) \( \operatorname{det}(-A)=\cdot \operatorname{det}(A) \) (ii) It A has two equal rows, then \( \operatorname{det}(\mathrm{A})=0 \) (iii) If \( \operatorname{det}(A)=0 \), then \( A \) has two equal rows. A. All of (i), (ii) and (iii) B. (ii) and (iii) C. (i) and (ii) D. (iii) E (i) and (iii)