Please help with matrices

(1/2) {ad - cb}  both expressions

Step-by-step explanation:

Notice that the area of the triangle in question can be calculated as the area of the larger right angle triangle OSQ MINUS the area of the smaller right angle triangle OPR, and MINUS the area of the trapezoid RSQP.

Given the coordinates of the given points, the formulas for area of triangles and of trapezoid, we have the following area subtractions:

1/2 (a + c) (b +d) - 1/2  a* b - 1/2  c (b + b + d)=

= (1/2) { ab + ad + cb + cd - ab - 2 cb -cd } =

= (1/2) {ad - cb}

On the other hand the matrix expression is giving you 1/2 of the determinant of the given matrix  such determinant is: ad - cb

Then we see that the equality is correct since (1/2) of the determinant is also :

(1/2) {ad - cb}

answer:

the position of equilibrium will shift to the left.

step-by-step explanation:

the general equation for the dissociation of a weak base is

b + h₂o   ⇌   bh⁺ + oh⁻

according to le châtelier's principle, when a stress is applied to a system at equilibrium, the system will respond in a way that tends to relieve the stress.

if you apply a stress by adding more bh⁺ or oh⁻,   the system will respond by moving in a direction that gets rid of the added ions.

the position of equilibrium will shift to the left, forming more of the undissociated base.