मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

If A = [731-2-41591], Find (AT)T.

Advertisements
Advertisements

प्रश्न

If A = `[(7, 3, 1),(-2, -4, 1),(5, 9, 1)]`, Find (AT)T.

बेरीज
Advertisements

उत्तर

A = `[(7, 3, 1),(-2, -4, 1),(5, 9, 1)]`

∴ AT = `[(7, -2, 5),(3, -4, 9),(1, 1, 1)]`

∴ (AT)T  = `[(7, 3, 1),(-2, -4, 1),(5, 9, 1)]`.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 4: Determinants and Matrices - Exercise 4.4 [पृष्ठ ८३]

APPEARS IN

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

 If A is a square matrix such that A2 = I, then find the simplified value of (A – I)3 + (A + I)3 – 7A.


Find the value of x, y, and z from the following equation:

`[(x + y + z), (x + z), (y + z)] = [(9), (5), (7)]`


`A = [a_(ij)]_(m xx n)` is a square matrix, if ______.


Let A = `[(0,1),(0,0)]`show that (aI+bA)n  = anI + nan-1 bA , where I is the identity matrix of order 2 and n ∈ N


if A = [(1,1,1),(1,1,1),(1,1,1)], Prove that A" = `[(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1))]` `n in N`


If A and B are square matrices of the same order such that AB = BA, then prove by induction that AB" = B"A. Further, prove that (AB)" = A"B" for all n ∈ N


Determine the product `[(-4,4,4),(-7,1,3),(5,-3,-1)][(1,-1,1),(1,-2,-2),(2,1,3)]` and use it to solve the system of equations x - y + z = 4, x- 2y- 2z = 9, 2x + y + 3z = 1.


Use product `[(1,-1,2),(0,2,-3),(3,-2,4)][(-2,0,1),(9,2,-3),(6,1,-2)]` to solve the system of equations x + 3z = 9, −x + 2y − 2z = 4, 2x − 3y + 4z = −3


Investigate for what values of λ and μ the equations
2x + 3y + 5z = 9
7x + 3y - 2z = 8
2x + 3y + λz = μ have
A. No solutions
B. Unique solutions
C. An infinite number of solutions.


If li, mi, ni, i = 1, 2, 3 denote the direction cosines of three mutually perpendicular vectors in space, prove that AAT = I, where \[A = \begin{bmatrix}l_1 & m_1 & n_1 \\ l_2 & m_2 & n_2 \\ l_3 & m_3 & n_3\end{bmatrix}\]


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"]`


Choose the correct alternative.

The matrix `[(8, 0, 0),(0, 8, 0),(0, 0, 8)]` is _______


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:

`[(5),(4),(-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:

`[(6, 0),(0, 6)]`


Identify the following matrix is singular or non-singular?

`[(5, 0, 5),(1, 99, 100),(6, 99, 105)]`


Identify the following matrix is singular or non-singular?

`[(3, 5, 7),(-2, 1, 4),(3, 2, 5)]`


Find k if the following matrix is singular:

`[("k" - 1, 2, 3),(3, 1, 2),(1, -2, 4)]`


If A = `[(1, 0),(-1, 7)]`, find k so that A2 – 8A – kI = O, where I is a unit matrix and O is a null matrix of order 2.


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 = diag [2 –3 –5], B = diag [4 –6 –3] and C = diag [–3 4 1] then find 2A + B – 5C


State whether the following statement is True or False:

If `[(3, 0),(0, 2)][(x),(y)] = [(3),(2)]`, then x = 1 and y = – 1


State whether the following statement is True or False:

If A and B are two square matrices such that AB = BA, then (A – B)2 = A2 – 2AB + B2 


If A = `[(2, 0, 0),(0, 1, 0),(0, 0, 1)]`, then |adj (A)| = ______


The matrix A = `[(0, 0, 5),(0, 5, 0),(5, 0, 0)]` is a ______.


If A and B are matrices of same order, then (3A –2B)′ is equal to______.


For the non singular matrix A, (A′)–1 = (A–1)′.


If `[("a","b"),("c", "-a")]`is a square root of the 2 x 2 identity matrix, then a, b, c satisfy the relation ____________.


For any square matrix A, AAT is a ____________.


If A `= [("cos x", - "sin x"),("sin x", "cos x")]`, find AAT.


If the matrix A `= [(5,2,"x"),("y",2,-3),(4, "t",-7)]` is a symmetric matrix, then find the value of x, y and t respectively.


A square matrix in which elements in the diagonal are all 1 and rest are all zero is called an


Find X, If `[X - 5 - 1] [(1, 0, 2),(0, 2, 1),(2, 0, 3)][(x),(4),(1)] ` = 0


How many matrices can be obtained by using one or more numbers from four given numbers?


Which general form represents a row matrix?


What is the order of a row matrix with \[n\] columns?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×