Question

If A, B, and C represent three matrices of the same size and (A + B) + C = 0, then which statement is true?

Answer 1

C

Explanation:

unit test review edge 2021

Answer 2

Statement c:

a₁₁ + ( b₁₁+ c₁₁ ) = 0

Explanation:

The options are:

a: a₁₁ = 0 and b₁₁ = 0

b: a₁₁ - ( b₁₁ + c₁₁ ) = 0

c. a₁₁ + ( b₁₁+ c₁₁ ) = 0

d. a₁₁x( b₁₁ + c₁₁) = 0

We know that A, B, and C are matrices of the same size, so we can write:

`A = \left[\begin{array}{ccc}a_(11)&a_(21)&...\\a_(21)&a_(22)&...\\...&...&...\end{array}\right]`

`B = \left[\begin{array}{ccc}b_(11)&b_(21)&...\\b_(21)&b_(22)&...\\...&...&...\end{array}\right]`

`C = \left[\begin{array}{ccc}c_(11)&c_(21)&...\\c_(21)&c_(22)&...\\...&...&...\end{array}\right]`

And here we have the sum of matrices, remember that:

And we know that (A + B) + C = 0 (a matrix full of zeros)

then:

`\left[\begin{array}{ccc}(a_(11) + b_(11)) + c_(11) &(a_(21) + b_(12)) + c_(12)&...\\(a_(21) + b_(21)) + c_(21)&(a_(22) + b_(22)) + c_(22)&...\\...&...&...\end{array}\right] = \left[\begin{array}{ccc}0&0&...\\0&...&...\\...&...&...\end{array}\right]`

Then:

(a₁₁ + b₁₁ )+ c₁₁ = 0

These are real numbers, so we can rewrite this as:

a₁₁ + ( b₁₁+ c₁₁ ) = 0

Then statement c is the correct one.