$$ A=\left[\begin{array}{cc}1 & -7 \ 9 & 3\end{array} ight] \quad B=\left[\begin{array}{cc}5 & -1 \ -7 & 7\end{array} ight] \quad C=\left[\begin{array}{cc}2 & -3 \ -7 & 1\end{array} ight] $$ $$ B A+C A=\left[\begin{array}{ll} ext { Ex: 42 } & \square \ \square & \square\end{array} ight] $$

Question

$$ A=\left[\begin{array}{cc}1 & -7 \ 9 & 3\end{array}ight] \quad B=\left[\begin{array}{cc}5 & -1 \ -7 & 7\end{array}ight] \quad C=\left[\begin{array}{cc}2 & -3 \ -7 & 1\end{array}ight] $$ $$ B A+C A=\left[\begin{array}{ll}	ext { Ex: 42 } & \square \ \square & \square\end{array}ight] $$

UpStudy AI · Accepted Answer

We want to compute

BA + CA

for

A = [ [1, –7],
      [9, 3] ],

B = [ [5, –1],
      [–7, 7] ], and

C = [ [2, –3],
      [–7, 1] ].

Notice that both terms in BA + CA have the same matrix A on the right, so we can factor it:
  BA + CA = (B + C) A.

Step 1. Find B + C.
  B + C = [ [5 + 2, –1 + (–3)],
        [–7 + (–7), 7 + 1] ]
      = [ [7, –4],
        [–14, 8] ].

Step 2. Multiply (B + C) and A.
We have:
  (B + C) A = [ [7, –4],
         [–14, 8] ]
         × [ [1, –7],
             [9, 3] ].

Now compute each entry:

• Top‑left entry:
  = (7 × 1) + (–4 × 9)
  = 7 – 36
  = –29.

• Top‑right entry:
  = (7 × –7) + (–4 × 3)
  = –49 – 12
  = –61.

• Bottom‑left entry:
  = (–14 × 1) + (8 × 9)
  = –14 + 72
  = 58.

• Bottom‑right entry:
  = (–14 × –7) + (8 × 3)
  = 98 + 24
  = 122.

Thus,
  BA + CA = [ [–29, –61],
         [58, 122] ].

This is the final answer.
$$ BA + CA = \left[ \begin{array}{cc} -29 & -61 \ 58 & 122 \end{array} ight] $$

\( A=\left[\begin{array}{cc}1 & -7 \\ 9 & 3\end{array}\right] \quad B=\left[\begin{array}{cc}5 & -1 \\ -7 & 7\end{array}\right] \quad C=\left[\begin{array}{cc}2 & -3 \\ -7 & 1\end{array}\right] \) \( B A+C A=\left[\begin{array}{ll}\text { Ex: 42 } & \square \\ \square & \square\end{array}\right] \)

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