Let A - - 3x2- 1- 6x - B - -a b c- and C - - x - 22 5x2 2x- 5x2 2x x - 22- 2x x-22 5x2 - be three given matrices- where a- b- c and x - R- Given that trAB - trC x - R- where trA denotes trace of A- If fx - ax2 - bx - c- then the value of f1 is -

AB=[ 3x^ 2; 1; 6x ][ a amp; b amp; c ] ⇒ AB=[ 3ax^ 2 amp; 3bx^ 2 amp; 3cx^ 2; a amp; b amp; c; 6ax am ...

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Addition and Subtraction of a Matrix

Let A = [ 3...

Question

Let $A = ⎡ ⎢ ⎣ \begin{matrix} 3 x^{2} 1 6 x \end{matrix} ⎤ ⎥ ⎦, B = [a b c]$ , and $C = ⎡ ⎢ ⎢ ⎣ \begin{matrix} (x + 2)^{2} & 5 x^{2} & 2 x 5 x^{2} & 2 x & (x + 2)^{2} 2 x & (x + 2)^{2} & 5 x^{2} \end{matrix} ⎤ ⎥ ⎥ ⎦$ be three given matrices, where a, b, c and x $\in$ R. Given that $t r (A B) = t r (C) x \in R,$ where tr(A) denotes trace of A. If $f (x) = a x^{2} + b x + c$ , then the value of f(1) is .................

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A = ⎡ ⎢ ⎣ \begin{matrix} 3 x^{2} 1 6 x \end{matrix} ⎤ ⎥ ⎦, B = [a, b, c]

C = ⎡ ⎢ ⎢ ⎣ \begin{matrix} (x + 2)^{2} & 5 x^{2} & 2 x 5 x^{2} & 2 x & (x + 2)^{2} 2 x & (x + 2)^{2} & 5 x^{2} \end{matrix} ⎤ ⎥ ⎥ ⎦

a, b, c

x \in R

t r . (A B) = t r . (C) \lor x \in R

t r . (A)

A

(a + b + c)

f (x) = a x^{2} + b x + c

a, b, c \in R

f (x)

x

x

f (x) = a x^{2} + b x + c, a, b, c \in R .

| f (x) | \leq 1, | x | \leq 1

| a + b |

\frac{8}{3} a^{2} + 2 b^{2}

f (x) = a x^{2} + b x + c, a, b, c \in R .

| f (x) | \leq 1, | x | \leq 1

\frac{8}{3} a^{2} + 2 b^{2}

A = [\begin{matrix} 2 & 1 4 & 1 \end{matrix}]

B = [\begin{matrix} 3 & 4 2 & 3 \end{matrix}]

C = [\begin{matrix} 3 & - 4 - 2 & 3 \end{matrix}]

t r (A) + t r (\frac{A B C}{2}) t r (\frac{A {(B C)}^{2}}{4}) + t r (\frac{A {(B C)}^{3}}{8}) + . . . . + \infty

t r (A)

A

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