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![🤔 Unknown Facts - Determinants For every square matrix A = [ai] of order n; we can associate a number called determinant of square matrix Itis denoted by AI det(A) Evaluating Determinants १) Order One (2) Order Two: A=[a] a11 a17 A= |A|=|a| a21 ೩22 ` a11 812 |4| =a11 ೩22 ೩12 ೩21 ` (3) Order Three: ೩21 ೩22' a11 ১13 d12 A= ১৯1 ೩22` ೩23 0 ১31 ೩32 d33 a11 ১12 313 ೩22 a21 ೩21 ` a23 03 ೩22 |4|= d12 + d13 821 872 ೩23 a11 832 d31 a31 ` ೩13 831 ೩12 ১31 012 ೩13 Properties Of Determinants (1) Property 1: Interchanging rows with columns (2) Property 2: Interchanging any wo TOWSI columns b2 (3) Property 3: When any [wo rowsl columns are equal b2 b 0 b2 b Determinants For every square matrix A = [ai] of order n; we can associate a number called determinant of square matrix Itis denoted by AI det(A) Evaluating Determinants १) Order One (2) Order Two: A=[a] a11 a17 A= |A|=|a| a21 ೩22 ` a11 812 |4| =a11 ೩22 ೩12 ೩21 ` (3) Order Three: ೩21 ೩22' a11 ১13 d12 A= ১৯1 ೩22` ೩23 0 ১31 ೩32 d33 a11 ১12 313 ೩22 a21 ೩21 ` a23 03 ೩22 |4|= d12 + d13 821 872 ೩23 a11 832 d31 a31 ` ೩13 831 ೩12 ১31 012 ೩13 Properties Of Determinants (1) Property 1: Interchanging rows with columns (2) Property 2: Interchanging any wo TOWSI columns b2 (3) Property 3: When any [wo rowsl columns are equal b2 b 0 b2 b - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_187744_39e588b8_1769354111180_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=180_sc.jpg "🤔 Unknown Facts - Determinants For every square matrix A = [ai] of order n; we can associate a number called determinant of square matrix Itis denoted by AI det(A) Evaluating Determinants १) Order One (2) Order Two: A=[a] a11 a17 A= |A|=|a| a21 ೩22 ` a11 812 |4| =a11 ೩22 ೩12 ೩21 ` (3) Order Three: ೩21 ೩22' a11 ১13 d12 A= ১৯1 ೩22` ೩23 0 ১31 ೩32 d33 a11 ১12 313 ೩22 a21 ೩21 ` a23 03 ೩22 |4|= d12 + d13 821 872 ೩23 a11 832 d31 a31 ` ೩13 831 ೩12 ১31 012 ೩13 Properties Of Determinants (1) Property 1: Interchanging rows with columns (2) Property 2: Interchanging any wo TOWSI columns b2 (3) Property 3: When any [wo rowsl columns are equal b2 b 0 b2 b Determinants For every square matrix A = [ai] of order n; we can associate a number called determinant of square matrix Itis denoted by AI det(A) Evaluating Determinants १) Order One (2) Order Two: A=[a] a11 a17 A= |A|=|a| a21 ೩22 ` a11 812 |4| =a11 ೩22 ೩12 ೩21 ` (3) Order Three: ೩21 ೩22' a11 ১13 d12 A= ১৯1 ೩22` ೩23 0 ১31 ೩32 d33 a11 ১12 313 ೩22 a21 ೩21 ` a23 03 ೩22 |4|= d12 + d13 821 872 ೩23 a11 832 d31 a31 ` ೩13 831 ೩12 ১31 012 ೩13 Properties Of Determinants (1) Property 1: Interchanging rows with columns (2) Property 2: Interchanging any wo TOWSI columns b2 (3) Property 3: When any [wo rowsl columns are equal b2 b 0 b2 b - ShareChat")
![🤔 Unknown Facts - Pythagorean Theorem a२ +62 Sine, Cosine, and Tangent Formulas (Remember: SOHCAHTOA] pposite Sin e hypotenuse hypotenuse adjacent opposite Cosine hypotenuse adjacent opposite' Tan gent . adjacent sudharsar Area ofa Triangle bh A= 10. Area of Rectangle A=bh 11. Area of Parallelogram 4=bh १० Area and Circumference of Circles A = 1T2 C= २r Pythagorean Theorem a२ +62 Sine, Cosine, and Tangent Formulas (Remember: SOHCAHTOA] pposite Sin e hypotenuse hypotenuse adjacent opposite Cosine hypotenuse adjacent opposite' Tan gent . adjacent sudharsar Area ofa Triangle bh A= 10. Area of Rectangle A=bh 11. Area of Parallelogram 4=bh १० Area and Circumference of Circles A = 1T2 C= २r - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_179178_a0da660_1769354087029_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=029_sc.jpg "🤔 Unknown Facts - Pythagorean Theorem a२ +62 Sine, Cosine, and Tangent Formulas (Remember: SOHCAHTOA] pposite Sin e hypotenuse hypotenuse adjacent opposite Cosine hypotenuse adjacent opposite' Tan gent . adjacent sudharsar Area ofa Triangle bh A= 10. Area of Rectangle A=bh 11. Area of Parallelogram 4=bh १० Area and Circumference of Circles A = 1T2 C= २r Pythagorean Theorem a२ +62 Sine, Cosine, and Tangent Formulas (Remember: SOHCAHTOA] pposite Sin e hypotenuse hypotenuse adjacent opposite Cosine hypotenuse adjacent opposite' Tan gent . adjacent sudharsar Area ofa Triangle bh A= 10. Area of Rectangle A=bh 11. Area of Parallelogram 4=bh १० Area and Circumference of Circles A = 1T2 C= २r - ShareChat")
![🤔 Unknown Facts - upper Triangular Matrix square matrix said to be a Upper triangular matrix if aij =0, if i >j (12 0 1 711 B= 021 ` 022 023 LLo 033_ 039 017 02] 1 @sudharsar 10 Lower Triangular Matrix square matrix said to be a Lower triangutar matrix if ೩ij =0, if i < j 011 B= 021 022 0131 _ 031 032 upper Triangular Matrix square matrix said to be a Upper triangular matrix if aij =0, if i >j (12 0 1 711 B= 021 ` 022 023 LLo 033_ 039 017 02] 1 @sudharsar 10 Lower Triangular Matrix square matrix said to be a Lower triangutar matrix if ೩ij =0, if i < j 011 B= 021 022 0131 _ 031 032 - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_24490_14f2e395_1769354002667_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=667_sc.jpg "🤔 Unknown Facts - upper Triangular Matrix square matrix said to be a Upper triangular matrix if aij =0, if i >j (12 0 1 711 B= 021 ` 022 023 LLo 033_ 039 017 02] 1 @sudharsar 10 Lower Triangular Matrix square matrix said to be a Lower triangutar matrix if ೩ij =0, if i < j 011 B= 021 022 0131 _ 031 032 upper Triangular Matrix square matrix said to be a Upper triangular matrix if aij =0, if i >j (12 0 1 711 B= 021 ` 022 023 LLo 033_ 039 017 02] 1 @sudharsar 10 Lower Triangular Matrix square matrix said to be a Lower triangutar matrix if ೩ij =0, if i < j 011 B= 021 022 0131 _ 031 032 - ShareChat")
![🤔 Unknown Facts - Inequalities Inequality Number Line terval Notation T > ০ Y<4 [Q,00) Y>( (~co, a] X = a (Qb) Q<1<ు (@,b] 0<1=1 [a,b) a_1<b Ia,b] 0<1<b Inequalities Inequality Number Line terval Notation T > ০ Y<4 [Q,00) Y>( (~co, a] X = a (Qb) Q<1<ు (@,b] 0<1=1 [a,b) a_1<b Ia,b] 0<1<b - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_980699_28dcab13_1769353972507_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=507_sc.jpg "🤔 Unknown Facts - Inequalities Inequality Number Line terval Notation T > ০ Y<4 [Q,00) Y>( (~co, a] X = a (Qb) Q<1<ు (@,b] 0<1=1 [a,b) a_1<b Ia,b] 0<1<b Inequalities Inequality Number Line terval Notation T > ০ Y<4 [Q,00) Y>( (~co, a] X = a (Qb) Q<1<ు (@,b] 0<1=1 [a,b) a_1<b Ia,b] 0<1<b - ShareChat")
![🤔 Unknown Facts - Circumlerence 0f circle: 0 = 2Tr = T0 Area 0f circle: A = Tr? Area of triangle: A= bh 0r 2 2 ab sin] 1 A =2 bc sin Aor A 2 ac sin B or A= Pythagorean theorem: a' + b' = c' @sudhcTsc1 VIX 7 - x١ + ٥٧، - ٧،١ Distance formula: 0 = फ+") X1 + X2 Midpoint formulaः M = 2 Y= Y Slope formula: m = X= Xi Equation of circle (x- 1? + Iy- k?=7 0" ೧೦' Degreelradian equivalence 180% Arc length $ = ०f r Circumlerence 0f circle: 0 = 2Tr = T0 Area 0f circle: A = Tr? Area of triangle: A= bh 0r 2 2 ab sin] 1 A =2 bc sin Aor A 2 ac sin B or A= Pythagorean theorem: a' + b' = c' @sudhcTsc1 VIX 7 - x١ + ٥٧، - ٧،١ Distance formula: 0 = फ+") X1 + X2 Midpoint formulaः M = 2 Y= Y Slope formula: m = X= Xi Equation of circle (x- 1? + Iy- k?=7 0" ೧೦' Degreelradian equivalence 180% Arc length $ = ०f r - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_811964_3026cf68_1769010810201_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=201_sc.jpg "🤔 Unknown Facts - Circumlerence 0f circle: 0 = 2Tr = T0 Area 0f circle: A = Tr? Area of triangle: A= bh 0r 2 2 ab sin] 1 A =2 bc sin Aor A 2 ac sin B or A= Pythagorean theorem: a' + b' = c' @sudhcTsc1 VIX 7 - x١ + ٥٧، - ٧،١ Distance formula: 0 = फ+\") X1 + X2 Midpoint formulaः M = 2 Y= Y Slope formula: m = X= Xi Equation of circle (x- 1? + Iy- k?=7 0\" ೧೦' Degreelradian equivalence 180% Arc length $ = ०f r Circumlerence 0f circle: 0 = 2Tr = T0 Area 0f circle: A = Tr? Area of triangle: A= bh 0r 2 2 ab sin] 1 A =2 bc sin Aor A 2 ac sin B or A= Pythagorean theorem: a' + b' = c' @sudhcTsc1 VIX 7 - x١ + ٥٧، - ٧،١ Distance formula: 0 = फ+\") X1 + X2 Midpoint formulaः M = 2 Y= Y Slope formula: m = X= Xi Equation of circle (x- 1? + Iy- k?=7 0\" ೧೦' Degreelradian equivalence 180% Arc length $ = ०f r - ShareChat")
![🤔 Unknown Facts - Sine The trigonometric function that is Sin]equal the ratio of the side opposite 0 giuen angle to the hypotemuse Cosine The trigonometric function that is Cos to the ratio of the side adjacent to an equal angle to the hypotenuse acutel Tongent A straight line or plane that | Tan touches a curve or curved surface at a point but if extended does not cross it at that point Cotangent The ratio of the side adjacent Csc particular acute angle to the side opposite 10 0 gf the angle Secant The ratio of the hypotenuset Sec to the shorter side odjocent to on Qcute angle; The reciprocal of a cosine The ratio of the hypotenuset Cosecant Cos to the side opposite an acute angle The reciprocal of sine TERMS OF TRGONOMETRY Sine The trigonometric function that is Sin]equal the ratio of the side opposite 0 giuen angle to the hypotemuse Cosine The trigonometric function that is Cos to the ratio of the side adjacent to an equal angle to the hypotenuse acutel Tongent A straight line or plane that | Tan touches a curve or curved surface at a point but if extended does not cross it at that point Cotangent The ratio of the side adjacent Csc particular acute angle to the side opposite 10 0 gf the angle Secant The ratio of the hypotenuset Sec to the shorter side odjocent to on Qcute angle; The reciprocal of a cosine The ratio of the hypotenuset Cosecant Cos to the side opposite an acute angle The reciprocal of sine TERMS OF TRGONOMETRY - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_580325_37e68e2d_1768403578851_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=851_sc.jpg "🤔 Unknown Facts - Sine The trigonometric function that is Sin]equal the ratio of the side opposite 0 giuen angle to the hypotemuse Cosine The trigonometric function that is Cos to the ratio of the side adjacent to an equal angle to the hypotenuse acutel Tongent A straight line or plane that | Tan touches a curve or curved surface at a point but if extended does not cross it at that point Cotangent The ratio of the side adjacent Csc particular acute angle to the side opposite 10 0 gf the angle Secant The ratio of the hypotenuset Sec to the shorter side odjocent to on Qcute angle; The reciprocal of a cosine The ratio of the hypotenuset Cosecant Cos to the side opposite an acute angle The reciprocal of sine TERMS OF TRGONOMETRY Sine The trigonometric function that is Sin]equal the ratio of the side opposite 0 giuen angle to the hypotemuse Cosine The trigonometric function that is Cos to the ratio of the side adjacent to an equal angle to the hypotenuse acutel Tongent A straight line or plane that | Tan touches a curve or curved surface at a point but if extended does not cross it at that point Cotangent The ratio of the side adjacent Csc particular acute angle to the side opposite 10 0 gf the angle Secant The ratio of the hypotenuset Sec to the shorter side odjocent to on Qcute angle; The reciprocal of a cosine The ratio of the hypotenuset Cosecant Cos to the side opposite an acute angle The reciprocal of sine TERMS OF TRGONOMETRY - ShareChat")
