Maths · Matrices, algebra of matrices, type of matrices
Assertion \left[\begin{array}{cc}\mathbf{1} & \mathbf{0} \\ -\mathbf{2} & \mathb
Assertion \( \mathbf{f}[\boldsymbol{x} \mathbf{1}]\left[\begin{array}{cc}\mathbf{1} & \mathbf{0} \\ -\mathbf{2} & \mathbf{3}\end{array}\right]\left[\begin{array}{c}\boldsymbol{x} \\ -\mathbf{5}\end{array}\right]=\mathbf{0}, \) then value of \( x \) is either- 3 or 5 Reason Two matrices \( \left[\begin{array}{ll}\boldsymbol{x} & \boldsymbol{y} \\ \boldsymbol{u} & \boldsymbol{v}\end{array}\right] \) \& \( \left[\begin{array}{ll}\boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{c} & \boldsymbol{d}\end{array}\right] \) are equal if \( \& \) only if their corresponding entries are equal \& only if their corresponding entries are equal
- A. Both (A) \& (R) are individually true \& (R) is correct explanation of (A)
- B. Both (A) \& (R) are individually true but (R) is not the correct (proper) explanation of (A).
- C. (A)is true but (R) is false
- D. (A)is false but (R) is true
Step-by-step solution
The assertion simplifies to x^2 - 2x - 15 = 0, giving x = 5 or x = -3, so the assertion is true. The reason is a correct statement about matrix equality but does not directly explain the solution of the matrix equation. Hence both are true but the reason is not the correct explanation.
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