MHB Is the Calculation of $(3 \diamond 8) \square 2 = 1940$ Correct?

Thread starter karush
Start date Nov 30, 2021
Tags

Binary Composite

Click For Summary

The binary operator $\diamond$ is defined as $a \diamond b = 4a + 4b$, and the operator $\square$ is defined as $a \square b = a^2 + b^2$. The calculation for $(3 \diamond 8) \square 2$ is performed as follows: first, $3 \diamond 8$ results in $44$, then $(44) \square 2$ computes to $44^2 + 2^2$. The final result is $1940$, confirming the calculation is correct. The conclusion is that the expression $(3 \diamond 8) \square 2 = 1940$ is accurate.

Nov 30, 2021

karush

Gold Member

MHB

define the binary operater $\diamond$ by
$a\diamond b$=4a+4b
and $s\square b$ by $a\square b=a^2+b^2$
find
$(3\diamond 8)\square 2=
[(4(3)+4(8))^2 +2^2]=1940$
ok just want to see if this is correct
before i run thru the ribbon :unsure:

Last edited: Dec 1, 2021

Mathematics news on Phys.org

Dec 1, 2021

Evgeny.Makarov

Gold Member

MHB

This is correct.

Dec 1, 2021

karush

Gold Member

MHB

1940

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...

View full post »