Evaluate the determinants in Exercises 1 and 2.
Answer :
= 2( - 1) - 4( - 5) = - 2 + 20 = 18
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Evaluate the determinants in Exercises 1 and 2.
(i) (ii)
Answer :
(i) = (cos θ)(cos θ) - ( - sin θ)(sin θ) = cos^{2} θ+ sin^{2} θ = 1
(ii)
= (x^{2} - x + 1)(x + 1) - (x - 1)(x + 1)
= x^{3} - x^{2} + x + x^{2} - x + 1 - (x^{2} - 1)
= x^{3} + 1 - x^{2} + 1
= x^{3} - x^{2} + 2
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If, then show that
Answer :
If, then show that
Answer :
Evaluate the determinants
(i) (iii)
(ii) (iv)
Answer :
Find values of x, if
(i) (ii)
Answer :
If, then x is equal to
(A) 6 (B) ±6 (C) - 6 (D) 0
Answer :
Using the property of determinants and without expanding, prove that:
Answer :
Using the property of determinants and without expanding, prove that:
Answer :
Using the property of determinants and without expanding, prove that:
Answer :
Using the property of determinants and without expanding, prove that:
Answer :
Using the property of determinants and without expanding, prove that:
Answer :
By using properties of determinants, show that:
Answer :
By using properties of determinants, show that:
Answer :
By using properties of determinants, show that:
(i)
(ii)
Answer :
By using properties of determinants, show that:
Answer :
By using properties of determinants, show that:
(i)
(ii)
Answer :
By using properties of determinants, show that:
(i)
(ii)
Answer :
By using properties of determinants, show that:
Answer :
By using properties of determinants, show that:
Answer :
By using properties of determinants, show that:
Answer :
Choose the correct answer.
Let A be a square matrix of order 3 × 3, then is equal to
A. B. C. D.
Answer :
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 :
Find area of the triangle with vertices at the point given in each of the following:
(i) (1, 0), (6, 0), (4, 3) (ii) (2, 7), (1, 1), (10, 8)
(iii) (-2, -3), (3, 2), (-1, -8)
Answer :
Show that points
are collinear
Answer :
Find values of k if area of triangle is 4 square units and vertices are
(i) (k, 0), (4, 0), (0, 2) (ii) (-2, 0), (0, 4), (0, k)
Answer :
(i) Find equation of line joining (1, 2) and (3, 6) using determinants
(ii) Find equation of line joining (3, 1) and (9, 3) using determinants
Answer :
If area of triangle is 35 square units with vertices (2, -6), (5, 4), and (k, 4). Then k is
A. 12 B. -2 C. -12, -2 D. 12, -2
Answer :
Write Minors and Cofactors of the elements of following determinants:
(i) (ii)
Answer :
Using Cofactors of elements of third column, evaluate
Answer :
If and A_{ij} is Cofactors of a_{ij}, then value of Δ is given by
Answer :
Find adjoint of each of the matrices.
Answer :
Find adjoint of each of the matrices.
Answer :
Verify A (adj A) = (adj A) A = I .
Answer :
Verify A (adj A) = (adj A) A = I .
Answer :
Find the inverse of each of the matrices (if it exists).
Answer :
Find the inverse of each of the matrices (if it exists).
Answer :
Find the inverse of each of the matrices (if it exists).
Answer :
Find the inverse of each of the matrices (if it exists).
Answer :
Find the inverse of each of the matrices (if it exists).
Answer :
Find the inverse of each of the matrices (if it exists).
.
Answer :
Find the inverse of each of the matrices (if it exists).
Answer :
Let and. Verify that
Answer :
If, show that. Hence find.
Answer :
For the matrix, find the numbers a and b such that A^{2} + aA + bI = O.
Answer :
For the matrixshow that A^{3} - 6A^{2} + 5A + 11 I = O. Hence, find A^{ - 1.}
Answer :
If verify that A^{3} - 6A^{2} + 9A - 4I = O and hence find A^{ - 1}
Answer :
Let A be a nonsingular square matrix of order 3 × 3. Then is equal to
A. B. C. D.
Answer :
If A is an invertible matrix of order 2, then det (A^{ - 1}) is equal to
A. det (A) B. C. 1 D. 0
Answer :
Examine the consistency of the system of equations.
x + 2y = 2
2x + 3y = 3
Answer :
Examine the consistency of the system of equations.
2x - y = 5
x + y = 4
Answer :
Examine the consistency of the system of equations.
x + 3y = 5
2x + 6y = 8
Answer :
Examine the consistency of the system of equations.
x +y + z = 1
2x + 3y + 2z = 2
ax + ay + 2az = 4
Answer :
Examine the consistency of the system of equations.
3x - y - 2z = 2
2y - z = -1
3x - 5y = 3
Answer :
Examine the consistency of the system of equations.
5x - y + 4z = 5
2x + 3y + 5z = 2
5x - 2y + 6z = -1
Answer :
Solve system of linear equations, using matrix method.
Answer :
Solve system of linear equations, using matrix method.
Answer :
Solve system of linear equations, using matrix method.
Answer :
Solve system of linear equations, using matrix method.
5x + 2y = 3
3x + 2y = 5
Answer :
Solve system of linear equations, using matrix method.
Answer :
Solve system of linear equations, using matrix method.
x - y + z = 4
2x + y - 3z = 0
x + y + z = 2
Answer :
Solve system of linear equations, using matrix method.
2x + 3y + 3z = 5
x - 2y + z = -4
3x - y - 2z = 3
Answer :
Solve system of linear equations, using matrix method.
x - y + 2z = 7
3x + 4y - 5z = -5
2x - y + 3z = 12
Answer :
If, find A^{ - 1}. Using A^{ - 1} solve the system of equations
Answer :
The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs 60. The cost of 2 kg onion, 4 kg
wheat and 6 kg rice is Rs 90. The cost of 6 kg onion 2 kg wheat and 3 kg rice is Rs 70.
Find cost of each item per kg by matrix method.
Answer :
Prove that the determinant is independent of θ.
Answer :
Without expanding the determinant, prove that
Answer :
If a, b and c are real numbers, and,
Show that either a + b + c = 0 or a = b = c.
Answer :
Solve the equations
Answer :
Let verify that
(i)
(ii)
Answer :
Using properties of determinants, prove that:
Answer :
Using properties of determinants, prove that:
Answer :
Using properties of determinants, prove that:
Answer :
Using properties of determinants, prove that:
Answer :
Using properties of determinants, prove that:
Answer :
Solve the system of the following equations
Answer :
Choose the correct answer.
If a, b, c, are in A.P., then the determinant
A. 0 B. 1 C. x D. 2x
Answer :
Choose the correct answer.
If x, y, z are nonzero real numbers, then the inverse of matrix is
A. B.
C. D.
Answer :
Choose the correct answer.
Let, where 0 ≤ θ≤ 2π, then
A. Det (A) = 0
B. Det (A) ∈ (2, ∞)
C. Det (A) ∈ (2, 4)
D. Det (A)∈ [2, 4]
Answer :
Maths Part-1 - Maths : CBSE NCERT Exercise Solutions for Class 12th for Determinants ( Exercise 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, miscellaneous ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.
Exercise 4.1 |
Question 1 |
Question 2 |
Question 3 |
Question 4 |
Question 5 |
Question 6 |
Question 7 |
Exercise 4.2 |
Question 1 |
Question 2 |
Question 3 |
Question 4 |
Question 5 |
Question 6 |
Question 7 |
Question 8 |
Question 9 |
Question 10 |
Question 11 |
Question 12 |
Question 13 |
Question 14 |
Question 15 |
Question 16 |
Exercise 4.3 |
Question 1 |
Question 2 |
Question 3 |
Question 4 |
Question 5 |
Exercise 4.4 |
Question 1 |
Question 2 |
Question 3 |
Question 4 |
Exercise 4.6 |
Question 1 |
Question 2 |
Question 3 |
Question 4 |
Question 5 |
Question 6 |
Question 7 |
Question 8 |
Question 9 |
Question 10 |
Question 11 |
Question 12 |
Question 13 |
Question 14 |
Question 15 |
Question 16 |