Question
If A =
and A2 + kI = 8A, then k equals
- 4
- 8
- ¼
- 1/16
The correct answer is: 8
To find the value of k.
Given, A =
and
+ kI = 8A.
x
+ k x
= 8 x ![open square brackets table row 3 1 row 7 5 end table close square brackets](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADIAAAAqCAYAAADxughHAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAaPUZr5AAAAXRJREFUeNrtmr9LQlEUxw8i4dASDo2BQzRICOLQENESEQ4iOEuLOIq7/4O7Y0PQ4CARbSJObY0hRLOLQ0M8RLDv5Z5BQlTeu97nsXPgs7xB7uf+ePe8LxLZmi9hV2vlWHd54JuI/W+Ra/ACfkAARqAN0iEHcgpa4N23SB+UwcHCsxx4DTmQB1CLsCucb61vl1skLpEM+JAscgzu+ZzcSRT5+x5vuH77+F6RI1ACb+BqH87IIcuIFyG+U8SLnPOBFyUyABWQBAm+6b9AVZrIJXjmrRTwTV/cVjerTaOKqIiKqIiKqIiKqIhMkfkaXPxOrCtiWvuOh7Z9qyImTRmClHSRHtm0kSSL1MlmtyRZ5IRsepIMOYAp2ajVhOJNsmlMLCID/maPUmYS8ryqJnY98y1S4Zl0WTc8Od5EEjx7OXJfgU+RUoiZ26Sy4NOnyCPZFD5KdcEFr67hliXKPkXGZAPsqJ2ASSdnYAKeQEGbxn0UEf2HgV/VqLr1+vOEzAAAAO90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZlbmNlZCBjbG9zZT0iXSIgb3Blbj0iWyIgc2VwYXJhdG9ycz0ifCI+PG10YWJsZT48bXRyPjxtdGQ+PG1uPjM8L21uPjwvbXRkPjxtdGQ+PG1uPjE8L21uPjwvbXRkPjwvbXRyPjxtdHI+PG10ZD48bW4+NzwvbW4+PC9tdGQ+PG10ZD48bW4+NTwvbW4+PC9tdGQ+PC9tdHI+PC9tdGFibGU+PC9tZmVuY2VkPjwvbWF0aD4sIIuQAAAAAElFTkSuQmCC)
+
= ![open square brackets table row 24 8 row 56 40 end table close square brackets](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEYAAAAqCAYAAAAOGC2lAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAaPUZr5AAAAuZJREFUeNrtmk9kXEEcx8eqiIrSQ1X1ECpqRVSpqoiqpSKqqkJU5Biqqqp6rR5LDz1UDmVF9NRLRERU9BK1KocQFTlElZ4iKpceYsWzQvv92e/a12fe7Ly8eX/I/Piy++a9ndnPm99v/vxGqbb91ei0mPG/nyYQNqA8GJdgxqAl6BBqQdvQjMVz9x2/gLPQHNSEAugLdLlIMA1oGhrg92Fog9fiTO7ddQxmAXoDnYH6oLfQZtlcaRDaMZTXoVnHYILI9wp7cOliTGBwvfUMYlkz1Gs7YPbKBmaU7hS1PvakwQzASHx5HmnDuzKB6advj2nKxO+fZTT6XaPrtBj3fkO3ywLmPLQCjcc0fMNUacqY9gm6xF4pdgP6xXoLBXOFUIZiyjc1Za7ALMcAqEFfiwRTheY5l0gy1Xa15AhOWJYpmIvQIucPqSpNYbsxPXWYsaYQMJ/ZY1SBYCYJp8ZhusLPEmOeFAUmjXu4HJWmoO8clQKOTA/9ItKvrj0YD8aD8WA8GA/Gg/FgPBgPxoMpF5iki8ib3KY45GJvFbqTouGm/NQ56INqb5KJ6ryWGxhbe0wQV0MNl+TctxNC6ZWfkmzEgwjE9bKBkU2jLcfd3JSfkm2IOc3198qcDMwdTD1hg3pZr/yUpI11m/I1lpUGzA/V3sV3YTb5qT+qmzGIPnuQF5gWg+ka9FL9nxHsWMDYIjv6R3xmS9kdAIiaTX7q2PB8Kw8wHZPNcMnlvGbvqGoqkK3He7y3Qnf4CT1NUI9tfsoEJsgTTNjEtxuRa9KjdMcyrkP7CX7bNj91EONK/Xm5ku1bWWMvcdG1beZOEmAnYl7aUlFgRlQ7dRE2cZdHmnurKv05Fl17JaUyr7n+Ma/hWoLpqOrmcyYIZVIzGjQ47+gk525xdLmbARgxSc++UN3DRK80Lp4ZmCkG0GMOkYuc9uvsAt9ik/dLI52fSAiZHDJYoFsfcS414BeRfnWdLxh/ADr03/8Ba0YcxACE1OAAAADjdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mZW5jZWQgY2xvc2U9Il0iIG9wZW49IlsiPjxtdGFibGU+PG10cj48bXRkPjxtbj4yNDwvbW4+PC9tdGQ+PG10ZD48bW4+ODwvbW4+PC9tdGQ+PC9tdHI+PG10cj48bXRkPjxtbj41NjwvbW4+PC9tdGQ+PG10ZD48bW4+NDA8L21uPjwvbXRkPjwvbXRyPjwvbXRhYmxlPjwvbWZlbmNlZD48L21hdGg+6y0oUwAAAABJRU5ErkJggg==)
comparing on both sides,
16+k=24
k=8
Therefore, the value of k is 8.
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