Compute the following-i bmatrix - b-b - alend bmatrix - bmatrix - b 1b - a e n d b m a t r i x a - 2- b - 2 - b - 2- c - 2 a - 2- c - 2 - a - 2- b - 2lendbmatrix - bmatrix 2 a b - 2 b c l l-2 a c -2 a b e n d b m a t r i x iii bmatrix -1 - 4 -6 18 - 5 - 16 12 - 8 - 511lend bmatrix - bmatrix 12 - 7 - 6 18 - 0 - 5113 - 2 - 4 lendbmatrix cos - 2 x -sin - 2 x lsin - 2 x -cos - 2 xlend bmatrix - bmatrix

[ a amp; b; b amp; a ]+[ a amp; b; b amp; a ]=[ a+a amp; b+b; b+b amp; a+a ]=[ 2a amp; 2b; 0 amp; 2a ] [ a^2+b^2 a ...

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Byju's Answer

Standard XII

Mathematics

Equality of Matrices

Compute the f...

Question

Compute the following:
$(i) [\begin{matrix} a & b - b & a \end{matrix}] + [\begin{matrix} a & b b & a \end{matrix}]$

$(i i) [\begin{matrix} a^{2} + b^{2} & b^{2} + c^{2} a^{2} + c^{2} & a^{2} + b^{2} \end{matrix}] + [\begin{matrix} 2 a b & 2 b c - 2 a c & - 2 a b \end{matrix}]$

$(i i i) ⎡ ⎢ ⎣ \begin{matrix} - 1 & 4 & - 6 8 & 5 & 16 2 & 8 & 5 \end{matrix} ⎤ ⎥ ⎦ + ⎡ ⎢ ⎣ \begin{matrix} 12 & 7 & 6 8 & 0 & 5 3 & 2 & 4 \end{matrix} ⎤ ⎥ ⎦$

$(i v) [\begin{matrix} c o s^{2} x & s i n^{2} x s i n^{2} x & c o s^{2} x \end{matrix}] + [\begin{matrix} s i n^{2} x & c o s^{2} x c o s^{2} x & s i n^{2} x \end{matrix}]$

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Solution

$[\begin{matrix} a & b - b & a \end{matrix}] + [\begin{matrix} a & b b & a \end{matrix}] = [\begin{matrix} a + a & b + b - b + b & a + a \end{matrix}] = [\begin{matrix} 2 a & 2 b 0 & 2 a \end{matrix}]$

$[\begin{matrix} a^{2} + b^{2} & b^{2} + c^{2} a^{2} + c^{2} & a^{2} + b^{2} \end{matrix}] + [\begin{matrix} 2 a b & 2 b c - 2 a c & - 2 a b \end{matrix}] = [\begin{matrix} a^{2} + b^{2} + 2 a b & b^{2} + c^{2} + 2 a b a^{2} + c^{2} - 2 a c & a^{2} + b^{2} - 2 a b \end{matrix}] = [\begin{matrix} (a + b)^{2} & (b + c)^{2} (a - c)^{2} & (a - b)^{2} \end{matrix}] [\begin{matrix} ∵ (a + b)^{2} = a^{2} + 2 a b + b^{2} (a - b)^{2} = a^{2} - 2 a b + b^{2} \end{matrix}]$

$⎡ ⎢ ⎣ \begin{matrix} - 1 & 4 & - 6 8 & 5 & 16 2 & 8 & 5 \end{matrix} ⎤ ⎥ ⎦ + ⎡ ⎢ ⎣ \begin{matrix} 12 & 7 & 6 8 & 0 & 5 3 & 2 & 4 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} - 1 + 12 & 4 + 7 & - 6 + 6 8 + 8 & 5 + 10 & 16 + 5 2 + 3 & 8 + 2 & 5 + 4 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 11 & 11 & 0 16 & 5 & 21 5 & 10 & 9 \end{matrix} ⎤ ⎥ ⎦$

$[\begin{matrix} c o s^{2} x & s i n^{2} x s i n^{2} x & c o s^{2} x \end{matrix}] + [\begin{matrix} s i n^{2} x & c o s^{2} x c o s^{2} x & s i n^{2} x \end{matrix}] = [\begin{matrix} c o s^{2} x + s i n^{2} x & s i n^{2} x + c o s^{2} x s i n^{2} x + c o s^{2} x & c o s^{2} x + s i n^{2} x \end{matrix}] = [\begin{matrix} 1 & 1 1 & 1 \end{matrix}] [∵ s i n^{2} x + c o s^{2} x = 1]$

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Similar questions

Compute the following:
$(i i) [\begin{matrix} a^{2} + b^{2} & b^{2} + c^{2} a^{2} + c^{2} & a^{2} + b^{2} \end{matrix}] + [\begin{matrix} 2 a b & 2 b c - 2 a c & - 2 a b \end{matrix}]$

Q. Given,

2 [\begin{matrix} 5 & 3 4 & 2 \end{matrix}] = [\begin{matrix} 10 & 6 8 & m \end{matrix}]

What is the value of m?

Show that $(i) [\begin{matrix} 5 & - 1 6 & 7 \end{matrix}] [\begin{matrix} 2 & 1 3 & 4 \end{matrix}] \neq [\begin{matrix} 2 & 1 3 & 4 \end{matrix}] [\begin{matrix} 5 & - 1 6 & 7 \end{matrix}]$

$(i i) ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 0 & 1 & 0 1 & 1 & 0 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} - 1 & 1 & 0 0 & - 1 & 1 2 & 3 & 4 \end{matrix} ⎤ ⎥ ⎦ \neq ⎡ ⎢ ⎣ \begin{matrix} - 1 & 1 & 0 0 & - 1 & 1 2 & 3 & 4 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 0 & 1 & 0 1 & 1 & 0 \end{matrix} ⎤ ⎥ ⎦$

Q. Write the matrix form for linear equations:

3 x + 4 y = 5 4 x + 5 y = 9

Q. Find the value of x, if

2 [\begin{matrix} 1 & 3 0 & x \end{matrix}] + [\begin{matrix} y & 0 1 & 2 \end{matrix}] = [\begin{matrix} 5 & 6 1 & 8 \end{matrix}]

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Compute the following: (i)[ab−ba]+[abba] (ii)[a2+b2b2+c2a2+c2a2+b2]+[2ab2bc−2ac−2ab] (iii)⎡⎢⎣−14−68516285⎤⎥⎦+⎡⎢⎣1276805324⎤⎥⎦ (iv)[cos2xsin2xsin2xcos2x]+[sin2xcos2xcos2xsin2x]