Find the best tutors and institutes for Class 12 Tuition
Search in
By using properties of determinants, show that:
(i)
(ii)
(i)
Applying R1 → R1 − R3 and R2 → R2 − R3, we have:
Applying R1 → R1 + R2, we have:
Expanding along C1, we have:
Hence, the given result is proved.
(ii) Let.
Applying C1 → C1 − C3 and C2 → C2 − C3, we have:
Applying C1 → C1 + C2, we have:
Expanding along C1, we have:
Hence, the given result is proved.
Choose the correct answer.
Let A be a square matrix of order 3 × 3, then is equal to
A. B. C. D.
Answer: C
A is a square matrix of order 3 × 3.
Hence, the correct answer is C.
By using properties of determinants, show that:
We have,
Here, the two rows R1 and R3 are identical.
∴Δ = 0.
Using the property of determinants and without expanding, prove that:
Using the property of determinants and without expanding, prove that:
Here, the two rows R1 and R3 are identical.
Δ = 0.
Using the property of determinants and without expanding, prove that:
Using the property of determinants and without expanding, prove that:
By applying C3 → C3 + C2, we have:
Here, two columns C1 and C3 are proportional.
Δ = 0.
Using the property of determinants and without expanding, prove that:
Applying R2 → R2 − R3, we have:
Applying R1 ↔R3 and R2 ↔R3, we have:
Applying R1 → R1 − R3, we have:
Applying R1 ↔R2 and R2 ↔R3, we have:
From (1), (2), and (3), we have:
Hence, the given result is proved.
By using properties of determinants, show that:
Applying R2 → R2 + R1 and R3 → R3 + R1, we have:
By using properties of determinants, show that:
(i)
(ii)
(i) Step 1
R1 = R1 + R2 + R3
Step 2
(5x+4) common in R1, bring that out, you are left with all 1s in R1
Applying C2 → C2 − C1, C3 → C3 − C1, we have:
Step 3
R2 = R2 - 2x(R1)
R3 = R3 - 2x(R1)
Now matrix is :
(5x+4)[(1,1,1),(0,4-x,0),(0,0,4-x)]
=(5x+4)(4-x)(4-x)
Expanding along C3, we have:
Hence, the given result is proved.
(ii) Here you need to subtract y(R1) from R2 and R3.
Applying R1 → R1 + R2 + R3, we have:
Applying C2 → C2 − C1 and C3 → C3 − C1, we have:
Expanding along C3, we have:
By using properties of determinants, show that:
(i)
(ii)
(i)
Applying R1 → R1 + R2 + R3, we have:
Applying C2 → C2 − C1, C3 → C3 − C1, we have:
Expanding along C3, we have:
Hence, the given result is proved.
(ii)
Applying C1 → C1 + C2 + C3, we have:
Applying R2 → R2 − R1 and R3 → R3 − R1, we have:
Expanding along R3, we have:
Hence, the given result is proved.
By using properties of determinants, show that:
Applying R1 → R1 + R2 + R3, we have:
Applying C2 → C2 − C1 and C3 → C3 − C1, we have:
Expanding along R1, we have:
Hence, the given result is proved.
By using properties of determinants, show that:
Applying R1 → R1 + bR3 and R2 → R2 − aR3, we have:
Expanding along R1, we have:
By using properties of determinants, show that:
Taking out common factors a, b, and c from R1, R2, and R3 respectively, we have:
Applying R2 → R2 − R1 and R3 → R3 − R1, we have:
Applying C1 → aC1, C2 → bC2, and C3 → cC3, we have:
Expanding along R3, we have:
Hence, the given result is proved.
Which of the following is correct?
A. Determinant is a square matrix.
B. Determinant is a number associated to a matrix.
C. Determinant is a number associated to a square matrix.
D. None of these
Answer: C
We know that to every square matrix, of order n. We can associate a number called the determinant of square matrix A, where element of A.
Thus, the determinant is a number associated to a square matrix.
Hence, the correct answer is C.
By using properties of determinants, show that:
Applying R2 → R2 − R1 and R3 → R3 − R1, we have:
Applying R3 → R3 + R2, we have:
Expanding along R3, we have:
Hence, the given result is proved.
How helpful was it?
How can we Improve it?
Please tell us how it changed your life *
Please enter your feedback
UrbanPro.com helps you to connect with the best Class 12 Tuition in India. Post Your Requirement today and get connected.
Find best tutors for Class 12 Tuition Classes by posting a requirement.
Get started now, by booking a Free Demo Class