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If A =  then A + AT is equal to ?

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Navik GD 26 April 2025 Memory-Based Paper (Section I + II)
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Detailed Solution

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Concept:

Transpose of a Matrix:

The new matrix obtained by interchanging the rows and columns of the original matrix is called the transpose of the matrix.

It is denoted by A′ or AT

Calculation:

Given:

A = 

Now find the transpose of a matrix A,

AT = 

Now,

A + AT = 

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Q1.If (AB + B)T = BTX  then X is equal to ?
Q2.If \(A - 2I = \begin{bmatrix} -1 & -2 & 3 \\\ 2 & 1 & -1 \\\ -3 & 1 & 0 \end{bmatrix}\) then find AAT where I is the identity matrix of order 3 × 3.
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Q1.What is A-1 equal to?  
Q2.What is A(adj A) equal to?  
Q3.Consider the following in respect of the matrices  \(\rm P=\begin{bmatrix}0&c&-b\\\ -c&0&a\\\ b&-a&0\end{bmatrix}\ and\ \rm Q=\begin{bmatrix}a^2&ab&ac\\\ ab&b^2&bc\\\ ac&bc&c^2\end{bmatrix}\) I. PQ is a null matrix.  II. QP is an identity matrix of order 3.  III. PQ = QP Which of the above is/are correct? 
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Q6.If \(A=\left[\begin{array}{cc} 1 & 3 \\ 0 & -1 \end{array}\right]\), then trace of 5A5 + 4A4 + 3A3 + 2A2 + A + I2 is :
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Q8.Let A and B be 3 × 3 real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear equations (A2B2 − B2A2)X = O, where X is a 3 × 1 column matrix of unknown variables and O is a 3 × 1 null matrix, has:
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