Consider
A=[53x−4−2x+814y+3−28−y6]A = \begin{bmatrix} 5 & 3x - 4 & -2 \\ x + 8 & 1 & 4y + 3 \\ -2 & 8 - y & 6 \end{bmatrix}A=5x+8−23x−418−y−24y+36
Recall that the transpose is defined entry by entry as (AT)i,j=Aj,i(A^{T})_{i,j} = A_{j,i}(AT)i,j=Aj,i.
Suppose the scalars xxx and yyy are chosen so that A=ATA = A^{T}A=AT — transposing leaves the matrix completely unchanged.
What is x+yx + yx+y?
Select all that apply.
333
777
000
No such xxx and yyy exist, because A=ATA = A^{T}A=AT would force the diagonal entries 555, 111 and 666 to be equal.