For the matrices A- 1 3- 0 -1 - B- 2 2- -1 4 -What is AB-

The correct option is E [ 1 14; 1 4 ] A and B are given by A=[ 1 amp; 3 0 amp; 1 ] , B=[ 2 amp; 2 1 amp; 4 ...

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Standard XII

Mathematics

Multiplication of Matrices

For the matri...

Question

For the matrices $A = [\begin{matrix} 1 & 3 0 & - 1 \end{matrix}]$ $B = [\begin{matrix} 2 & 2 - 1 & 4 \end{matrix}]$
What is $A B$ ?

[\begin{matrix} 3 & 5 - 1 & 3 \end{matrix}]

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[\begin{matrix} 1 & - 1 - 1 & 5 \end{matrix}]

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[\begin{matrix} - 1 & 14 1 & - 4 \end{matrix}]

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[\begin{matrix} 2 & 4 - 1 & - 7 \end{matrix}]

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none of the above

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Solution

The correct option is E $[\begin{matrix} - 1 & 14 1 & - 4 \end{matrix}]$
$A$ and $B$ are given by $A = [\begin{matrix} 1 & 3 0 & - 1 \end{matrix}], B = [\begin{matrix} 2 & 2 - 1 & 4 \end{matrix}]$
Thus, $A B = [\begin{matrix} (1 \times 2) + (3 \times - 1) & (1 \times 2) + (3 \times 4) (0 \times 2) + (- 1 \times - 1) & (0 \times 2) + (- 1 \times 4) \end{matrix}]$
$= [\begin{matrix} 2 - 3 & 2 + 12 0 + 1 & 0 - 4 \end{matrix}]$
$= [\begin{matrix} - 1 & 14 1 & - 4 \end{matrix}]$

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1, 15

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0, 15

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1, 14

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4,
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1,

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35 - {15 + 14 - (13 + ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ (2 - 1 + 3)}

\int \frac{x}{4 + x^{4}} d x

is equal to

(a)

\frac{1}{4} \tan^{- 1} x^{2} + C

(b)

\frac{1}{4} \tan^{- 1} (\frac{x^{2}}{2})

(c)

\frac{1}{2} \tan^{- 1} (\frac{x^{2}}{2})

(d) none of these

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For the matrices A=[130−1] B=[22−14]What is AB?

The correct option is E [−1141−4]A and B are given by A=[130−1],B=[22−14]Thus, AB=[(1×2)+(3×−1)(1×2)+(3×4)(0×2)+(−1×−1)(0×2)+(−1×4)]=[2−32+120+10−4]=[−1141−4]

For the matrices $A = [\begin{matrix} 1 & 3 0 & - 1 \end{matrix}]$ $B = [\begin{matrix} 2 & 2 - 1 & 4 \end{matrix}]$
What is $A B$ ?