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Ncert Solutions Maths class 12th Maths Class 12th Matrices

7. Find the value of a, b, c and d from the equation:

$[\begin{matrix} a - b & 2 a + c \\ 2 a - b & 3 c + d \end{matrix}] = [\begin{matrix} - 1 & 5 \\ 0 & 13 \end{matrix}]$

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Vishal Baghel | Contributor-Level 10

4 months ago

$[\begin{matrix} a - b & 2 a + c \\ 2 a - b & 3 c + d \end{matrix}] = [\begin{matrix} - 1 & 5 \\ 0 & 13 \end{matrix}]$

(5) Equating the corresponding elements of the matrices we get,

a - b = -1 - (i)

2a + c = 5 - (2)

2a - b = 0 - (3)

3c + d = 13 - (4)

Subtracting eqⁿ (1) from (3) we get,

2a - b (a - b) = 0- (-1)

2a - b - a+ b = 0 + 1 = 1

$\Rightarrow$ [a= 1]

Put $a = 1 eq^{n} (2)$ we get,

2 × 1 + c = 5 $\Rightarrow$ c = 5 - 2 $\Rightarrow$ [c = 3]

Put $c = 3 q^{n}$ (4) we get,

3 × 3 + d = 13 => d = 13 - 9 $\Rightarrow$ [d = 4.]

put $a = 1 q^{2} (1)$ we get, 1 - b = -1 $\Rightarrow$ b = 1 + 1 $\Rightarrow$ [b= 2]

<math><mrow><mrow><mo> [</mo><mrow><mtable><mtr columnalign="center"><mtd columnalign="center"><mi>a</mi><mo>−</mo><mi>b</mi></mtd><mtd columnalign="center"><mn>2</mn><mi>a</mi><mo>+</mo><mi>c</mi></mtd></mtr><mtr columnalign="center"><mtd columnalign="center"><mn>2</mn><mi>a</mi><mo>−</mo><mi>b</mi></mtd><mtd columnalign="center"><mn>3</mn><mi>c</mi><mo>+</mo><mi>d</mi></mtd></mtr></mtable></mrow><mo>]</mo></mrow><mo>=</mo><mrow><mo> [</mo><mrow><mtable><mtr columnalign="center"><mtd columnalign="center"><mo>−</mo><mn>1</mn></mtd><mtd columnalign="center"><mn>5</mn></mtd></mtr><mtr columnalign="center"><mtd columnalign="center"><mn>0</mn></mtd><mtd columnalign="center"><mn>1</mn><mn>3</mn></mtd></mtr></mtable></mrow><mo>]</mo></mrow></mrow></math> (5) Equating the corresponding elements of the matrices we get, a - b = -1 - (i)2a + c = 5 - (2)2a - b = 0 - (3)3c + d = 13 - (4)Subtracting eqn (1) from (3) we get, 2a - b (a - b) = 0- (-1)2a - b - a+ b = 0 + 1 = 1<math><mrow><mo>⇒</mo></mrow></math>  [a= 1]Put <math><mrow><mi>a</mi><mo>=</mo><mn>1 eq</mn><mtext> </mtext><msup><mrow></mrow><mrow><mi>n</mi></mrow></msup><mo stretchy="false"> (</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></math> we get, 2 × 1 + c = 5 <math><mrow><mo>⇒</mo></mrow></math> c = 5 - 2 <math><mrow><mo>⇒</mo></mrow></math>  [c = 3]Put <math><mrow><mi>c</mi><mo>=</mo><mn>3</mn><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><msup><mrow><mi>q</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></math>  (4) we get, 3 × 3 + d = 13  => d = 13 - 9 <math><mrow><mo>⇒</mo></mrow></math>  [d = 4.]put <math><mrow><mi>a</mi><mo>=</mo><mn>1</mn><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy="false"> (</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></math> we get, 1 - b = -1 <math><mrow><mo>⇒</mo></mrow></math> b = 1 + 1 <math><mrow><mo>⇒</mo></mrow></math>  [b= 2]

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7. Find the value of a, b, c and d from the equation:

$[\begin{matrix} a - b & 2 a + c \\ 2 a - b & 3 c + d \end{matrix}] = [\begin{matrix} - 1 & 5 \\ 0 & 13 \end{matrix}]$

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7. Find the value of a, b, c and d from the equation: [a−b2a+c2a−b3c+d]=[−15013]

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7. Find the value of a, b, c and d from the equation:

$[\begin{matrix} a - b & 2 a + c \\ 2 a - b & 3 c + d \end{matrix}] = [\begin{matrix} - 1 & 5 \\ 0 & 13 \end{matrix}]$