Advertisements
Advertisements
Question
Let A be a square matrix of order 3 × 3, then | kA| is equal to
(A) k|A|
(B) k2 | A |
(C) k3 | A |
(D) 3k | A |
Advertisements
Solution
Answer: C
A is a square matrix of order 3 × 3.

Hence, the correct answer is C.
APPEARS IN
RELATED QUESTIONS
Using the property of determinants and without expanding, prove that:
`|(x, a, x+a),(y,b,y+b),(z,c, z+ c)| = 0`
Without expanding at any stage, find the value of:
`|(a,b,c),(a+2x,b+2y,c+2z),(x,y,z)|`
Use properties of determinants to solve for x:
`|(x+a, b, c),(c, x+b, a),(a,b,x+c)| = 0` and `x != 0`
On expanding by first row, the value of the determinant of 3 × 3 square matrix
\[A = \left[ a_{ij} \right]\text{ is }a_{11} C_{11} + a_{12} C_{12} + a_{13} C_{13}\] , where [Cij] is the cofactor of aij in A. Write the expression for its value on expanding by second column.
Let A = [aij] be a square matrix of order 3 × 3 and Cij denote cofactor of aij in A. If |A| = 5, write the value of a31 C31 + a32 C32 a33 C33.
A matrix of order 3 × 3 has determinant 2. What is the value of |A (3I)|, where I is the identity matrix of order 3 × 3.
A matrix A of order 3 × 3 is such that |A| = 4. Find the value of |2 A|.
If A is a 3 × 3 invertible matrix, then what will be the value of k if det(A–1) = (det A)k.
Which of the following is not correct?
Using matrices, solve the following system of linear equations :
x + 2y − 3z = −4
2x + 3y + 2z = 2
3x − 3y − 4z = 11
Without expanding, show that Δ = `|("cosec"^2theta, cot^2theta, 1),(cot^2theta, "cosec"^2theta, -1),(42, 40, 2)|` = 0
The determinant ∆ = `|(sqrt(23) + sqrt(3), sqrt(5), sqrt(5)),(sqrt(15) + sqrt(46), 5, sqrt(10)),(3 + sqrt(115), sqrt(15), 5)|` is equal to ______.
The determinant ∆ = `|(cos(x + y), -sin(x + y), cos2y),(sinx, cosx, siny),(-cosx, sinx, cosy)|` is independent of x only.
Prove tha `|("bc" - "a"^2, "ca" - "b"^2, "ab" - "c"^2),("ca" - "b"^2, "ab" - "c"^2, "bc" - "a"^2),("ab" - "c"^2, "bc" - "a"^2, "ca" - "b"^2)|` is divisible by a + b + c and find the quotient.
Let f(t) = `|(cos"t","t", 1),(2sin"t", "t", 2"t"),(sin"t", "t", "t")|`, then `lim_("t" - 0) ("f"("t"))/"t"^2` is equal to ______.
If x, y, z are all different from zero and `|(1 + x, 1, 1),(1, 1 + y, 1),(1, 1, 1 + z)|` = 0, then value of x–1 + y–1 + z–1 is ______.
There are two values of a which makes determinant, ∆ = `|(1, -2, 5),(2, "a", -1),(0, 4, 2"a")|` = 86, then sum of these number is ______.
If A is a matrix of order 3 × 3, then |3A| = ______.
If A is invertible matrix of order 3 × 3, then |A–1| ______.
`|(0, xyz, x - z),(y - x, 0, y z),(z - x, z - y, 0)|` = ______.
If A and B are matrices of order 3 and |A| = 5, |B| = 3, then |3AB| = 27 × 5 × 3 = 405.
The maximum value of `|(1, 1, 1),(1, (1 + sintheta), 1),(1, 1, 1 + costheta)|` is `1/2`
`"A" = abs ((1/"a", "a"^2, "bc"),(1/"b", "b"^2, "ac"),(1/"c", "c"^2, "ab"))` is equal to ____________.
`abs ((1 + "a", "b", "c"),("a", 1 + "b", "c"),("a", "b", 1 + "c")) =` ____________
The value of the determinant `abs ((1,0,0),(2, "cos x", "sin x"),(3, "sin x", "cos x"))` is ____________.
If `Delta = abs((5,3,8),(2,0,1),(1,2,3)),` then write the minor of the element a23.
If `"abc" ne 0 "and" abs ((1 + "a", 1, 1),(1, 1 + "b", 1),(1,1,1 + "c")) = 0, "then" 1/"a" + 1/"b" + 1/"c" =` ____________.
Let A be a square matrix of order 2 x 2, then `abs("KA")` is equal to ____________.
For positive numbers x, y, z the numerical value of the determinant `|(1, log_x y, log_x z),(log_y x, 3, log_y z),(log_z x, log_z y, 5)|` is
For positive numbers x, y, z, the numerical value of the determinant `|(1, log_x y, log_x z),(log_y x, 1, log_y z),(log_z x, log_z y, 1)|` is
