Question

Type the correct answer in each box.If matrix C represents (A − B) + A, the value of the entry represented by c41 is and the corresponding entry in (A + B) − A is .

Answer 1

Given the matrices A and B:

`\begin{gathered} A=\begin{bmatrix}{-5} & {3} & {8} & {} \\ {3} & {6} & {-5} & {} \\ {5} & {-9} & {0} & {} \\ {7} & {3} & {4} & {}\end{bmatrix} \\ \\ B=\begin{bmatrix}{-7} & {-8} & {-5} & {} \\ {7} & {9} & {2} & {} \\ {2} & {5} & {-7} & {} \\ {2} & {8} & {-7} & {}\end{bmatrix} \end{gathered}`

We know that:

`C=(A-B)+A=2A-B`

Then, using the matrices A and B:

`\begin{gathered} C=2\cdot\begin{bmatrix}{-5} & {3} & {8} & {} \\ {3} & {6} & {-5} & {} \\ {5} & {-9} & {0} & {} \\ {7} & {3} & {4} & {}\end{bmatrix}-\begin{bmatrix}{-7} & {-8} & {-5} & {} \\ {7} & {9} & {2} & {} \\ {2} & {5} & {-7} & {} \\ {2} & {8} & {-7} & {}\end{bmatrix} \\ \\ C=\begin{bmatrix}{-10} & {6} & {16} & {} \\ 6 & {12} & {-10} & {} \\ 10 & {-18} & {0} & {} \\ 14 & 6 & 8 & {}\end{bmatrix}+\begin{bmatrix}{7} & {8} & {5} & {} \\ -{7} & -{9} & -{2} & {} \\ -{2} & {-5} & {7} & {} \\ {-2} & -{8} & {7} & {}\end{bmatrix} \\ \\ \therefore C=\begin{bmatrix}{-3} & 14 & 21 & {} \\ -1 & {3} & {-12} & {} \\ 8 & {-23} & 7 & {} \\ 12 & -2 & 15 & {}\end{bmatrix} \end{gathered}`

And the element C₄₁ (fourth row and first column) is:

`C_(41)=12`

Now, for the matrix (A + B) - A = B:

`B_(41)=2`