SATHEE: Matrices and Determinants 1 Question 9

Matrices and Determinants 1 Question 9

9. If $A = [\begin{array}{ll} α & 0 \\ 1 & 1 \end{array}]$ and $B = [\begin{array}{ll} 1 & 0 \\ 5 & 1 \end{array}]$ then value of $α$ for which $A^{2} = B$ , is

(2003, 1M)

(a) 1

(b) -1

(d) no real values

Show Answer

Answer:

Correct Answer: 9. (d)

Solution:

$\begin{array}{ll} Given, & A = [\begin{array}{ll} α & 0 \\ 1 & 1 \end{array}], B = [\begin{array}{ll} 1 & 0 \\ 5 & 1 \end{array}] \\ \Rightarrow & A^{2} = [\begin{array}{ll} α & 0 \\ 1 & 1 \end{array}] [\begin{array}{ll} α & 0 \\ 1 & 1 \end{array}] = [\begin{array}{ll} α^{2} & 0 \\ α + 1 & 1 \end{array}] \end{array}$

Also, given, $A^{2} = B$

$\begin{aligned} \Rightarrow [\begin{array}{ll} α^{2} & 0 \\ α + 1 & 1 \end{array}] = [\begin{array}{ll} 1 & 0 \\ 5 & 1 \end{array}] \\ \Rightarrow α^{2} = 1 and α + 1 = 5 \end{aligned}$

Which is not possible at the same time.

$∴$ No real values of $α$ exists.

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Matrices and Determinants 1 Question 9

9. If A=[α011] and B=[1051] then value of α for which A2=B, is

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9. If $A = [\begin{array}{ll} α & 0 \\ 1 & 1 \end{array}]$ and $B = [\begin{array}{ll} 1 & 0 \\ 5 & 1 \end{array}]$ then value of $α$ for which $A^{2} = B$ , is