Find the value of determinant a h g h b f g f c

To evaluate: a h g h b f g f c Expanding along the first row, we get a h g h b f g f c = a b f f c - h h f g c + g h b g f = a b c - f 2 - h h c - f g + g h f - b g = a b c - a f 2 - h 2 c + h f g + g h f - b g 2 = a b c + 2 f g h - a f 2 - b g 2 - c h 2 Hence, the value of given determinant is a b c + 2 f g h - a f 2 - b g 2 - c h 2 .

Find the value of x if x 2 - x + 1 x + 1 x + 1 x + 1 = 0 .

Given, x 2 - x + 1 x + 1 x + 1 x + 1 = 0 ∴ x 2 - x + 1 x + 1 - x + 1 x + 1 = 0 ⇒ x + 1 x 2 - x + 1 - x - 1 = 0 ⇒ x + 1 x 2 - 2 x = 0 ⇒ x x + 1 x - 2 = 0 ⇒ x = 0 or x + 1 = 0 or x - 2 = 0 ⇒ x = 0 , x = - 1 , x = 2 Hence, x = 0 , x = - 1 , x = 2

E M B I B E

Mathematics and Statistics (Arts & Science) Part 1>Chapter 4 - Determinants and Matrices>EXERCISE 4.1

Maharashtra Board Solutions for Chapter: Determinants and Matrices, Exercise 1: EXERCISE 4.1

Author:Maharashtra Board

Maharashtra Board Mathematics Solutions for Exercise - Maharashtra Board Solutions for Chapter: Determinants and Matrices, Exercise 1: EXERCISE 4.1

Attempt the practice questions on Chapter 4: Determinants and Matrices, Exercise 1: EXERCISE 4.1 with hints and solutions to strengthen your understanding. Mathematics and Statistics (Arts & Science) Part 1 solutions are prepared by Experienced Embibe Experts.

Questions from Maharashtra Board Solutions for Chapter: Determinants and Matrices, Exercise 1: EXERCISE 4.1 with Hints & Solutions

EASY

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 1>Chapter 4 - Determinants and Matrices>EXERCISE 4.1>Q 1

Find the value of determinant $|\begin{array}{r} 2 i & 3 \\ 4 & - i \end{array}|$

EASY

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 1>Chapter 4 - Determinants and Matrices>EXERCISE 4.1>Q 1

Find the value of determinant $|\begin{array}{r} 3 & - 4 & 5 \\ 1 & 1 & - 2 \\ 2 & 3 & 1 \end{array}|$

EASY

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 1>Chapter 4 - Determinants and Matrices>EXERCISE 4.1>Q 1

Find the value of determinant $|\begin{array}{lll} a & h & g \\ h & b & f \\ g & f & c \end{array}|$

EASY

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 1>Chapter 4 - Determinants and Matrices>EXERCISE 4.1>Q 2

Find the value of $x$ if $|\begin{matrix} x^{2} - x + 1 & x + 1 \\ x + 1 & x + 1 \end{matrix}| = 0$ .

EASY

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 1>Chapter 4 - Determinants and Matrices>EXERCISE 4.1>Q 2

Find the value of $x$ if $|\begin{array}{r} x & - 1 & 2 \\ 2 x & 1 & - 3 \\ 3 & - 4 & 5 \end{array}| = 29$

MEDIUM

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 1>Chapter 4 - Determinants and Matrices>EXERCISE 4.1>Q 4

Find the minor and cofactor of element of the determinant

$D = |\begin{array}{r} 2 & - 1 & 3 \\ 1 & 2 & - 1 \\ 5 & 7 & 2 \end{array}|$

HARD

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 1>Chapter 4 - Determinants and Matrices>EXERCISE 4.1>Q 5

Evaluate $A = |\begin{matrix} 2 & - 3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & - 7 \end{matrix}|$ , also find minor and cofactor of elements in $2^{nd}$ row of determinant and verify $a_{21} C_{21} + a_{22} C_{22} + a_{23} C_{23} =$ value of $A$ , where $C_{21}, C_{22}, C_{23}$ are cofactor of $a_{21}, a_{22}, a_{23}$ .