Advertisements
Advertisements
प्रश्न
if `vec"a"= 2hat"i" + 3hat"j"+ hat"k", vec"b" = hat"i" -2hat"j" + hat"k" and vec"c" = -3hat"i" + hat"j" + 2hat"k", "find" [vec"a" vec"b" vec"c"]`
Advertisements
उत्तर
`[vec" a" vec" b" vec" c"]`
= `|(2,3,1),(1,-2,1),(-3,1,2)|`
= 2 (- 4 - 1) - 3 (2+3) + 1 (1 - 6)
= - 30
APPEARS IN
संबंधित प्रश्न
If A is a square matrix, such that A2=A, then write the value of 7A−(I+A)3, where I is an identity matrix.
Find the value of x, y, and z from the following equation:
`[(x+y+z), (x+z), (y+z)] = [(9),(5),(7)]`
If A = `[(alpha, beta),(gamma, -alpha)]` is such that A2 = I then ______.
Given two matrices A and B
`A = [(1,-2,3),(1,4,1),(1,-3, 2)] and B = [(11,-5,-14),(-1, -1,2),(-7,1,6)]`
find AB and use this result to solve the following system of equations:
x - 2y + 3z = 6, x + 4x + z = 12, x - 3y + 2z = 1
In a certain city there are 30 colleges. Each college has 15 peons, 6 clerks, 1 typist and 1 section officer. Express the given information as a column matrix. Using scalar multiplication, find the total number of posts of each kind in all the colleges.
Using coding matrix A=`[(2,1),(3,1)]` encode the message THE CROW FLIES AT MIDNIGHT.
Show that (A + A') is symmetric matrix, if `A = ((2,4),(3,5))`
Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:
`[(10, -15, 27),(-15, 0, sqrt(34)),(27, sqrt(34), 5/3)]`
Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:
`[(1, 0, 0),(0, 1, 0),(0, 0, 1)]`
Identify the following matrix is singular or non-singular?
`[(3, 5, 7),(-2, 1, 4),(3, 2, 5)]`
Identify the following matrix is singular or non-singular?
`[(7, 5),(-4, 7)]`
Select the correct option from the given alternatives:
If A and B are square matrices of equal order, then which one is correct among the following?
Answer the following question:
If A = `[(1, 2),(3, 2),(-1, 0)]` and B = `[(1, 3, 2),(4, -1, -3)]`, show that AB is singular.
Answer the following question:
If A = `[(1, omega),(omega^2, 1)]`, B = `[(omega^2, 1),(1, omega)]`, where ω is a complex cube root of unity, then show that AB + BA + A −2B is a null matrix
If A = `[(6, 0),("p", "q")]` is a scalar matrix, then the values of p and q are ______ respectively.
Choose the correct alternative:
If A = `[(2, 0),(0, 2)]`, then A2 – 3I = ______
State whether the following statement is True or False:
If A is non singular, then |A| = 0
The matrix A = `[(0, 0, 5),(0, 5, 0),(5, 0, 0)]` is a ______.
For the non singular matrix A, (A′)–1 = (A–1)′.
If A = `[(3, -4),(1, 1),(2, 0)]` and B = `[(2, 1, 2),(1, 2, 4)]`, then verify (BA)2 ≠ B2A2
If `[("a","b"),("c", "-a")]`is a square root of the 2 x 2 identity matrix, then a, b, c satisfy the relation ____________.
If A is a square matrix, then A – A’ is a ____________.
If A `= [("cos x", - "sin x"),("sin x", "cos x")]`, find AAT.
The matrix `[(0,-5,8),(5,0,12),(-8,-12,0)]` is a ____________.
A = `[a_(ij)]_(m xx n)` is a square matrix, if
Find X, If `[X - 5 - 1] [(1, 0, 2),(0, 2, 1),(2, 0, 3)][(x),(4),(1)] ` = 0
Assertion: Let the matrices A = `((-3, 2),(-5, 4))` and B = `((4, -2),(5, -3))` be such that A100B = BA100
Reason: AB = BA implies AB = BA for all positive integers n.
