If A- 8 5 2- 1 -3 4 - then find A T and A T T-

Given, A=[ 8 amp; 5 amp; 2; 1 amp; 3 amp; 4 ] A ^ T =[ 8 amp; 1; 5 amp; 3; 2 amp; 4 ] Therefore, ( A ^ T ) ...

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Byju's Answer

Standard XII

Mathematics

Transpose of a Matrix

If A=[ 8 5 ...

Question

If $A = (\begin{matrix} 8 & 5 & 2 1 & - 3 & 4 \end{matrix})$ , then find $A^{T}$ and ${(A^{T})}^{T}$ .

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Solution

Given, $A = (\begin{matrix} 8 & 5 & 2 1 & - 3 & 4 \end{matrix})$
$A^{T} = ⎛ ⎜ ⎝ \begin{matrix} 8 & 1 5 & - 3 2 & 4 \end{matrix} ⎞ ⎟ ⎠$
Therefore, ${(A^{T})}^{T} = (\begin{matrix} 8 & 5 & 2 1 & - 3 & 4 \end{matrix})$

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Similar questions

Q. If

A = (\begin{matrix} 8 & 5 & 2 1 & - 3 & 4 \end{matrix})

then find

A^{T}

and

(A^{T})^{T}

Q. If

A = (\begin{matrix} 1 & 2 & 3 2 & 4 & - 5 3 & - 5 & 6 \end{matrix})

, then verify that

(A^{T})^{T} = A

Consider a matrix A. Then $(A^{T})^{T}$ = ___

If $A = [\begin{matrix} 12 - 13 \end{matrix}] B = [\begin{matrix} 4015 \end{matrix}] C = [\begin{matrix} 20 1 - 2 \end{matrix}]$ ,
a = 4, and b = - 2, then show that:

(i) A + (B + C) = (A + B) + C

(ii) A (BC) = (AB) C

(iii) (a + b)B = aB + bB

(iv) a (C - A) = aC - aA

(v) $(A^{T})^{T}$ = A

(vi) $(b A)^{T}$ = b $A^{T}$

(vii) $(A B)^{T} = B^{T} A^{T}$

(viii) (A - B)C = AC - BC

(ix) $(A - B)^{T} = A^{T} - B^{T}$

Q. If

A^{T} = ⎡ ⎢ ⎣ \begin{matrix} 3 & 4 - 1 & 2 0 & 1 \end{matrix} ⎤ ⎥ ⎦

and

B = [\begin{matrix} - 1 & 2 & 1 1 & 2 & 3 \end{matrix}]

, then find

A^{T} - B^{T} .

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If A=(8521−34), then find AT and (AT)T.

Given, A=(8521−34)AT=⎛⎜⎝815−324⎞⎟⎠Therefore, (AT)T=(8521−34)

If $A = (\begin{matrix} 8 & 5 & 2 1 & - 3 & 4 \end{matrix})$ , then find $A^{T}$ and ${(A^{T})}^{T}$ .

Given, $A = (\begin{matrix} 8 & 5 & 2 1 & - 3 & 4 \end{matrix})$
$A^{T} = ⎛ ⎜ ⎝ \begin{matrix} 8 & 1 5 & - 3 2 & 4 \end{matrix} ⎞ ⎟ ⎠$
Therefore, ${(A^{T})}^{T} = (\begin{matrix} 8 & 5 & 2 1 & - 3 & 4 \end{matrix})$