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.
Practise more in this unitView MCQsSign up for full question bank