If the matrix A = [[0, 5], [5, 0]], find A transpose.

A. pmatrix 0 & 5 5 & 0 pmatrix — The transpose of a matrix is obtained by interchanging its rows and columns. Since the element at (1,2) is 5 and the element at (2,1) is 5, interchanging them results in the same matrix.

C. pmatrix 0 & -5 -5 & 0 pmatrix

JEE Main · MathematicsEasy

$If the matrix A = (0550), find A^{T} .$

A. $(0550)$
B. $(5005)$
C. $(0 - 5 - 5 0)$
D. $(0505)$

Show correct answer & step-by-step solution

Correct answer: A — $(0550)$

Solution

The transpose of a matrix is obtained by interchanging its rows and columns. Since A_{12} = 5 and A_{21} = 5, interchanging them results in the same matrix A^{T} = A .

Attempt this question & track your score

Attempt & Track Free →

More Matrices & Determinants practice questions

$What is the value of the determinant of an identity matrix of order 3?$
$If A is a square matrix such that A squared equals A, then A is called what?$
$If a matrix A has 12 elements, what are the possible orders it can have?$
$Find the value of the determinant of the matrix [[2, 4], [-1, 2]].$
$T h e v a l u eo f t h e d e t er minan t o f t h e ma t r i x [[1, a, a^{2}], [1, b, b^{2}], [1, c, c^{2}]] i s :$
$I f A = [[cos t h e t a, - s in t h e t a], [s in t h e t a, cos t h e t a]], t h e n A^{n} i se q u a l t o :$
$I f A i s a 3 x 3 ma t r i x s u c h t ha t A^{2} = A an d I i s t h e i d e n t i t y ma t r i x, t h e n t h e v a l u eo f (I + A)^{n} i se q u a l t o :$
$If the system of equations x + y + z = 6, x + 2y + 3z = 10, and x + 2y + lambda z = mu has no solution, then:$
$I f A i s a s q u a r e ma t r i x s u c h t ha t A^{T} A = I, t h e n t h e d e t er minan t o f A i s :$
$I f A i s a s k e w - sy mm e t r i c ma t r i x o f or d er 3, t h e n t h e v a l u eo f t h e d e t er minan t o f A^{4} i s a l w a y se q u a l t o :$
$If the system of equations x + y + z = 6, x + 2y + 3z = 10, and x + 2y + kz = m has no solution, then:$
$L e t A b e a 3 x 3 ma t r i x s u c h t ha t A^{T} A = I an dd e t (A) = 1. T h e n d e t (A - I) i se q u a l t o :$

View all Matrices & Determinants questions →

If the matrix A=(05​50​), find AT.

Solution

Attempt this question & track your score

More Matrices & Determinants practice questions

$If the matrix A = (0550), find A^{T} .$