Question

$a = \binom{1 \: \: \: 3}{4 \: \: \: 5} \\ b = \binom{12 \: \: \: 9}{7 \: \: \ \: 6} \\ find \: {a}^{t} + {b}^{t} \\ i \: want \: a \: written \: solution \: no \: adding \: of \: pictures. \: answers \: with \: pictures \: will \: be \: deleted.$
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Answer 1

$\binom{13 \: \: \: 11}{12 \: \: \: 11}$

Step-by-step explanation:

$First \: you \: should \: know \: the \: formula \\ of \: transpose \\ Lemme \: give \: you \: an \: example.... \\ if \: \:X= \binom{a \: \: \: b}{c \: \: \: d} \\ then \: {X}^{t} = \binom{a \: \: \: c}{b \: \: \: d}$

$Applying \: this \: formula \: in \\ \: your \: question... \\A= \binom{1 \: \: \: 3}{4 \: \: \: 5} \\ \: So, \: {A}^{t} = \binom{1 \: \: \: 4}{3 \: \: \: 5} \\ B = \binom{12 \: \: \: 9}{7 \: \: \: 6} \\ {B}^{t} = \binom{12 \: \: \: 7}{9 \: \: \: 6} \\ Before \: adding \: the \: two \: matrix \: \\ lemme \: add \: another \: formula.. \\ if \: X = \binom{a \: \: b}{c \: \: d} \\ and \: Y = \binom{e \: \: f}{g \: \: h} \\ then \: X+Y = \binom{(a + e) \: \: \: (b + f)}{(c + g) \: \: \: (d + h)} \\ Applying \: this \: formula \\ {A}^{t} + {B}^{t} = \binom{(1 + 12) \: \: (4 + 7)}{(3 + 9) \: \: (5 + 6)} \\ = > \binom{13 \: \: \: 11}{12 \: \: \: 11} \\ \bold Hence \: this \: is \: the \: Answer$

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Note :-

• Plural of matrix is called matrices.
• Each number or entity in a matrix is called as its element.
• In a matrix, the horizontal lines are called rows, whereas the vertical lines are called columns.

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