Using the cross product we have

Determinant

**i j k**0 1 01 1 1

=**i**(1*1-0*1)-**j**(0*1-0*1)+**k**(0*1-1*1)=**i**-**k**

We could also use distribution to get

**j**x(**i**+**j**+**k**)=**j**x**i**+**j**x**j**+**j**x**k**=-**k**+0+**i**=**i**-**k**

Using the cross product we have

Determinant

**i j k**

0 1 0

1 1 1

=**i**(1*1-0*1)-**j**(0*1-0*1)+**k**(0*1-1*1)=**i**-**k**

We could also use distribution to get

**j**x(**i**+**j**+**k**)=**j**x**i**+**j**x**j**+**j**x**k**=-**k**+0+**i**=**i**-**k**