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Algebra of Matrices — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices2 Marks
Question
If $\begin{bmatrix}\text{x}+3&\text{z}+4&2\text{y}-7\\4\text{x}+6&\text{a}-1&0\\\text{b}-3&3\text{b}&\text{z}+2\text{c}\end{bmatrix}=\begin{bmatrix}0&6&3\text{y}-2\\2\text{x}&-3&2\text{c}-2\\2\text{b}+4&-21&0\end{bmatrix}$ Obtain the values of a, b, c, x, y and z.
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Answer

Since all the corresponding elements of a matrix are equal, x + 3 = 0 ⇒ x = -3 Also, 2y - 7 = 3y - 2 ⇒ 2y - 3y = -2 + 7 ⇒ -y = 5 ⇒ y = -5⇒ z + 4 = 6
⇒ z = 6 - 4 ⇒ z = 2⇒ a - 1 = -3
⇒ a = -3 + 1 ⇒ a = -2 3b = -21 ⇒ b = -7⇒ z + 2c = 0
⇒ 2 = -2c ⇒ c = -1 Thus, x = -3, y = -5, a = -2, b = -7 and c = -1

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